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Recent questions tagged differentiation
7
votes
2
answers
31
GO Classes CS Test Series 2025 | Calculus | Topic Wise Test 3 | Question: 8
Choose the CORRECT statement - The function $f(x)=\exp \left(-x^{2}\right)-1$ has the root $x=0$. If a function $f$ is differentiable on $[-1,1]$, then there is a point $x$ in that interval where $f^{\prime}(x)=0$. If ... $f^{\prime \prime}(1)>0$ then there is a point in $(0,1)$, where $f$ has an inflection point.
Choose the CORRECT statement -The function $f(x)=\exp \left(-x^{2}\right)-1$ has the root $x=0$.If a function $f$ is differentiable on $[-1,1]$, then there is a point $x$...
GO Classes
1.0k
views
GO Classes
asked
Aug 28, 2022
Calculus
goclasses_2025_cs_em_tw_3
goclasses
calculus
differentiation
multiple-selects
1-mark
+
–
3
votes
1
answer
32
GO Classes CS Test Series 2025 | Calculus | Topic Wise Test 3 | Question: 9
Evaluate $y^{\prime \prime}(1)$ where $y=e^{x}+x^{e}$. $0$ $1$ $e^{2}$ $e$
Evaluate $y^{\prime \prime}(1)$ where $y=e^{x}+x^{e}$.$0$$1$$e^{2}$$e$
GO Classes
458
views
GO Classes
asked
Aug 28, 2022
Calculus
goclasses_2025_cs_em_tw_3
goclasses
calculus
differentiation
1-mark
+
–
7
votes
1
answer
33
GO Classes CS Test Series 2025 | Calculus | Topic Wise Test 3 | Question: 11
Let $I=(a, b)$ be an open interval and let $f$ be a function which is differentiable on $I$. Which of the followings is/are true statements - If $f^{\prime}(x)=0$ for all $x \in I$, then there is a constant $r$ ... on $I$. If $f^{\prime}(x)>0$ for all $x \in I$, then $f(x)$ is strictly decreasing on $I$.
Let $I=(a, b)$ be an open interval and let $f$ be a function which is differentiable on $I$. Which of the followings is/are true statements -If $f^{\prime}(x)=0$ for all ...
GO Classes
612
views
GO Classes
asked
Aug 28, 2022
Calculus
goclasses_2025_cs_em_tw_3
goclasses
calculus
differentiation
maxima-minima
multiple-selects
2-marks
+
–
8
votes
1
answer
34
GO Classes CS Test Series 2025 | Calculus | Topic Wise Test 3 | Question: 12
Which of the following is/are FALSE? The absolute maximum value of $f(x)=\dfrac{1}{x}$ on the interval $[2,4]$ is $2.$ If $f(x)$ is a continuous function and $f(3)=2$ and $f(5)=-1$, then $f(x)$ has a root between $3$ ... $h(1)=4$ and $h(2)=5$, then $h(x)$ has no roots between $1$ and $2.$
Which of the following is/are FALSE?The absolute maximum value of $f(x)=\dfrac{1}{x}$ on the interval $[2,4]$ is $2.$If $f(x)$ is a continuous function and $f(3)=2$ and $...
GO Classes
631
views
GO Classes
asked
Aug 28, 2022
Calculus
goclasses_2025_cs_em_tw_3
goclasses
calculus
differentiation
maxima-minima
multiple-selects
2-marks
+
–
6
votes
1
answer
35
GO Classes CS Test Series 2025 | Calculus | Topic Wise Test 3 | Question: 13
Suppose $g(x)$ is a polynomial function such that $g(-1)=4$ and $g(2)=7$. Then there is a number $c$ between $-1$ and $2$ such that $g(c)=1$ $g^{\prime}(c)=1$ $g(c)=0$ $g^{\prime}(c)=0$
Suppose $g(x)$ is a polynomial function such that $g(-1)=4$ and $g(2)=7$. Then there is a number $c$ between $-1$ and $2$ such that$g(c)=1$$g^{\prime}(c)=1$$g(c)=0$$g^{\p...
GO Classes
715
views
GO Classes
asked
Aug 28, 2022
Calculus
goclasses_2025_cs_em_tw_3
goclasses
calculus
differentiation
maxima-minima
2-marks
+
–
6
votes
1
answer
36
GO Classes CS Test Series 2025 | Calculus | Topic Wise Test 3 | Question: 15
Suppose $f$ is twice differentiable with $ f^{\prime \prime}(x)=7 x-2, \quad f^{\prime}(-2)=0, \quad \text { and } \quad f(-2)=-2 . $ Find $f(0)$. $-337 / 6$ $-74 / 3$ $23 / 9$ $37 / 4$
Suppose $f$ is twice differentiable with$$f^{\prime \prime}(x)=7 x-2, \quad f^{\prime}(-2)=0, \quad \text { and } \quad f(-2)=-2 .$$Find $f(0)$.$-337 / 6$$-74 / 3$$23 / 9...
GO Classes
599
views
GO Classes
asked
Aug 28, 2022
Calculus
goclasses_2025_cs_em_tw_3
goclasses
calculus
differentiation
2-marks
+
–
4
votes
1
answer
37
GO Classes CS Test Series 2025 | Calculus | Topic Wise Test 3 | Question: 16
The sum of three positive numbers is $12$ and two of them are equal. Find the largest possible product. $86$ $64$ $48$ $72$
The sum of three positive numbers is $12$ and two of them are equal. Find the largest possible product.$86$$64$$48$$72$
GO Classes
539
views
GO Classes
asked
Aug 28, 2022
Calculus
goclasses_2025_cs_em_tw_3
goclasses
calculus
differentiation
maxima-minima
2-marks
+
–
3
votes
2
answers
38
GO Classes CS Test Series 2025 | Calculus | Topic Wise Test 3 | Question: 17
If $f(x)=e^{x} g(x), g(0)=2$ and $g^{\prime}(0)=1$, then $f^{\prime}(0)$ is $1$ $3$ $2$ $0$
If $f(x)=e^{x} g(x), g(0)=2$ and $g^{\prime}(0)=1$, then $f^{\prime}(0)$ is$1$$3$$2$$0$
GO Classes
429
views
GO Classes
asked
Aug 28, 2022
Calculus
goclasses_2025_cs_em_tw_3
goclasses
calculus
differentiation
maxima-minima
2-marks
+
–
6
votes
1
answer
39
GO Classes CS Test Series 2025 | Calculus | Topic Wise Test 3 | Question: 18
Let $f$ be differentiable for all $x$. If $f(1)=-2$ and $f^{\prime}(x) \geq 2$ for $x \in[1,6]$, then $f(6) \geq 8$ $f(6)<8$ $f(6)<5$ $f(6)=5$
Let $f$ be differentiable for all $x$. If $f(1)=-2$ and $f^{\prime}(x) \geq 2$ for $x \in[1,6]$, then$f(6) \geq 8$$f(6)<8$$f(6)<5$$f(6)=5$
GO Classes
490
views
GO Classes
asked
Aug 28, 2022
Calculus
goclasses_2025_cs_em_tw_3
goclasses
calculus
differentiation
maxima-minima
2-marks
+
–
8
votes
1
answer
40
GO Classes CS Test Series 2025 | Calculus | Topic Wise Test 3 | Question: 19
The equation $x^{5}+x+1=0$ has a solution in the interval $[0,1]$ $[-1,0]$ $[-2,-1]$ $[1,2]$
The equation $x^{5}+x+1=0$ has a solution in the interval$[0,1]$$[-1,0]$$[-2,-1]$$[1,2]$
GO Classes
560
views
GO Classes
asked
Aug 28, 2022
Calculus
goclasses_2025_cs_em_tw_3
goclasses
calculus
differentiation
maxima-minima
2-marks
+
–
0
votes
0
answers
41
Best Open Video Playlist for Differentiability Topic | Calculus
Please list out the best free available video playlist for Differentiability Topic from Calculus as an answer here (only one playlist per answer). We'll then select the best playlist and add to GO classroom video lists. You ... ones are more likely to be selected as best. For the full list of selected videos please see here
Please list out the best free available video playlist for Differentiability Topic from Calculus as an answer here (only one playlist per answer). We'll then select the b...
makhdoom ghaya
155
views
makhdoom ghaya
asked
Aug 15, 2022
Study Resources
missing-videos
free-videos
video-links
go-classroom
differentiation
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0
votes
1
answer
42
Applied Mathematics Derivative
Please find derivation of the following equation. Let $f(x)=e^{x^{2}}\ln x,$ then find, ${f}'(x)$.
Please find derivation of the following equation.Let $f(x)=e^{x^{2}}\ln x,$ then find, ${f}'(x)$.
kidussss
328
views
kidussss
asked
Jul 8, 2022
Calculus
calculus
differentiation
+
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0
votes
3
answers
43
Applied Mathematics Question
Let $f(x) = e^{x^2},$ then find $f''(x).$
Let $f(x) = e^{x^2},$ then find $f''(x).$
kidussss
459
views
kidussss
asked
Jul 7, 2022
Calculus
calculus
differentiation
+
–
0
votes
0
answers
44
TIFR-2016-Maths-A: 4
Let $f:\mathbb{R}\rightarrow \mathbb{R}$ be the function defined by $f\left ( x \right )=\frac{\sin \: x}{\left | x \right |+\cos \: x}$. Then $f$ is differentiable at all $x\in\mathbb{R}$ $f$ is not differentiable at $x=0$ $f$ is differentiable at $x=0$ but ${f}'$ is not continuous at $x=0$ $f$ is not differentiable at $x=\frac{\pi }{2}.$
Let $f:\mathbb{R}\rightarrow \mathbb{R}$ be the function defined by $f\left ( x \right )=\frac{\sin \: x}{\left | x \right |+\cos \: x}$. Then $f$ is differentiable at al...
soujanyareddy13
188
views
soujanyareddy13
asked
Aug 30, 2020
Others
tifrmaths2016
differentiation
calculus
+
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2
votes
1
answer
45
ISI2014-DCG-13
Let the function $f(x)$ be defined as $f(x)=\mid x-1 \mid + \mid x-2 \:\mid$. Then which of the following statements is true? $f(x)$ is differentiable at $x=1$ $f(x)$ is differentiable at $x=2$ $f(x)$ is differentiable at $x=1$ but not at $x=2$ none of the above
Let the function $f(x)$ be defined as $f(x)=\mid x-1 \mid + \mid x-2 \:\mid$. Then which of the following statements is true?$f(x)$ is differentiable at $x=1$$f(x)$ is di...
Arjun
573
views
Arjun
asked
Sep 23, 2019
Calculus
isi2014-dcg
calculus
differentiation
+
–
0
votes
2
answers
46
ISI2014-DCG-29
If $f(x) = \sin \bigg( \dfrac{1}{x^2+1} \bigg),$ then $f(x)$ is continuous at $x=0$, but not differentiable at $x=0$ $f(x)$ is differentiable at $x=0$, and $f’(0) \neq 0$ $f(x)$ is differentiable at $x=0$, and $f’(0) = 0$ None of the above
If $f(x) = \sin \bigg( \dfrac{1}{x^2+1} \bigg),$ then$f(x)$ is continuous at $x=0$, but not differentiable at $x=0$$f(x)$ is differentiable at $x=0$, and $f’(0) \neq 0$...
Arjun
731
views
Arjun
asked
Sep 23, 2019
Calculus
isi2014-dcg
calculus
continuity
differentiation
+
–
0
votes
1
answer
47
ISI2014-DCG-49
Let $f(x) = \dfrac{x}{(x-1)(2x+3)}$, where $x>1$. Then the $4^{th}$ derivative of $f, \: f^{(4)} (x)$ is equal to $- \frac{24}{5} \bigg[ \frac{1}{(x-1)^5} - \frac{48}{(2x+3)^5} \bigg]$ ... $\frac{64}{5} \bigg[ \frac{1}{(x-1)^5} + \frac{48}{(2x+3)^5} \bigg]$
Let $f(x) = \dfrac{x}{(x-1)(2x+3)}$, where $x>1$. Then the $4^{th}$ derivative of $f, \: f^{(4)} (x)$ is equal to$- \frac{24}{5} \bigg[ \frac{1}{(x-1)^5} – \frac{48}{(2...
Arjun
686
views
Arjun
asked
Sep 23, 2019
Others
isi2014-dcg
calculus
differentiation
functions
+
–
0
votes
2
answers
48
ISI2015-MMA-69
Consider the function $f(x) = \begin{cases} \int_0^x \{5+ \mid 1-y \mid \} dy & \text{ if } x>2 \\ 5x+2 & \text{ if } x \leq 2 \end{cases}$ Then $f$ is not continuous at $x=2$ $f$ is continuous and differentiable everywhere $f$ is continuous everywhere but not differentiable at $x=1$ $f$ is continuous everywhere but not differentiable at $x=2$
Consider the function $$f(x) = \begin{cases} \int_0^x \{5+ \mid 1-y \mid \} dy & \text{ if } x>2 \\ 5x+2 & \text{ if } x \leq 2 \end{cases}$$ Then$f$ is not continuous at...
Arjun
844
views
Arjun
asked
Sep 23, 2019
Calculus
isi2015-mma
calculus
continuity
differentiation
definite-integral
non-gate
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–
0
votes
1
answer
49
ISI2015-MMA-72
The map $f(x) = a_0 \cos \mid x \mid +a_1 \sin \mid x \mid +a_2 \mid x \mid ^3$ is differentiable at $x=0$ if and only if $a_1=0$ and $a_2=0$ $a_0=0$ and $a_1=0$ $a_1=0$ $a_0, a_1, a_2$ can take any real value
The map $f(x) = a_0 \cos \mid x \mid +a_1 \sin \mid x \mid +a_2 \mid x \mid ^3$ is differentiable at $x=0$ if and only if$a_1=0$ and $a_2=0$$a_0=0$ and $a_1=0$$a_1=0$$a_0...
Arjun
504
views
Arjun
asked
Sep 23, 2019
Calculus
isi2015-mma
calculus
differentiation
+
–
0
votes
1
answer
50
ISI2015-MMA-73
$f(x)$ is a differentiable function on the real line such that $\underset{x \to \infty=}{\lim} f(x) =1$ and $\underset{x \to \infty=}{\lim} f’(x) =\alpha$. Then $\alpha$ must be $0$ $\alpha$ need not be $0$, but $\mid \alpha \mid <1$ $\alpha >1$ $\alpha < -1$
$f(x)$ is a differentiable function on the real line such that $\underset{x \to \infty=}{\lim} f(x) =1$ and $\underset{x \to \infty=}{\lim} f’(x) =\alpha$. Then$\alpha$...
Arjun
492
views
Arjun
asked
Sep 23, 2019
Calculus
isi2015-mma
calculus
limits
differentiation
+
–
0
votes
1
answer
51
ISI2015-MMA-74
Let $f$ and $g$ be two differentiable functions such that $f’(x)\leq g’(x)$for all $x<1$ and $f’(x) \geq g’(x)$ for all $x>1$. Then if $f(1) \geq g(1)$, then $f(x) \geq g(x)$ for all $x$ if $f(1) \leq g(1)$, then $f(x) \leq g(x)$ for all $x$ $f(1) \leq g(1)$ $f(1) \geq g(1)$
Let $f$ and $g$ be two differentiable functions such that $f’(x)\leq g’(x)$for all $x<1$ and $f’(x) \geq g’(x)$ for all $x>1$. Thenif $f(1) \geq g(1)$, then $f(x)...
Arjun
429
views
Arjun
asked
Sep 23, 2019
Calculus
isi2015-mma
calculus
differentiation
+
–
0
votes
2
answers
52
ISI2015-DCG-57
Let $y=\lfloor x \rfloor$, where $\lfloor x \rfloor$ is greatest integer less than or equal to $x$. Then $y$ is continuous and many-one $y$ is not differentiable and many-one $y$ is not differentiable $y$ is differentiable and many-one
Let $y=\lfloor x \rfloor$, where $\lfloor x \rfloor$ is greatest integer less than or equal to $x$. Then$y$ is continuous and many-one$y$ is not differentiable and many-o...
gatecse
449
views
gatecse
asked
Sep 18, 2019
Calculus
isi2015-dcg
calculus
continuity
differentiation
+
–
0
votes
0
answers
53
ISI2016-DCG-58
Let $y=\left \lfloor x \right \rfloor$ where $\left \lfloor x \right \rfloor$ is greatest integer less than or equal to $x$. Then $y$ is continuous and many-one. $y$ is not differentiable and many-one. $y$ is not differentiable. $y$ is differentiable and many-one.
Let $y=\left \lfloor x \right \rfloor$ where $\left \lfloor x \right \rfloor$ is greatest integer less than or equal to $x$. Then$y$ is continuous and many-one.$y$ is not...
gatecse
393
views
gatecse
asked
Sep 18, 2019
Calculus
isi2016-dcg
calculus
continuity
differentiation
functions
+
–
1
votes
2
answers
54
ISI2017-DCG-30
If $f(x)=e^{5x}$ and $h(x)=f’’(x)+2f’(x)+f(x)+2$ then $h(0)$ equals $38$ $8$ $4$ $0$
If $f(x)=e^{5x}$ and $h(x)=f’’(x)+2f’(x)+f(x)+2$ then $h(0)$ equals$38$$8$$4$$0$
gatecse
343
views
gatecse
asked
Sep 18, 2019
Calculus
isi2017-dcg
calculus
differentiation
functions
+
–
2
votes
1
answer
55
ISI2018-DCG-9
Let $f(x)=1+x+\dfrac{x^2}{2}+\dfrac{x^3}{3}...+\dfrac{x^{2018}}{2018}.$ Then $f’(1)$ is equal to $0$ $2017$ $2018$ $2019$
Let $f(x)=1+x+\dfrac{x^2}{2}+\dfrac{x^3}{3}...+\dfrac{x^{2018}}{2018}.$ Then $f’(1)$ is equal to $0$$2017$$2018$$2019$
gatecse
659
views
gatecse
asked
Sep 18, 2019
Calculus
isi2018-dcg
calculus
functions
differentiation
+
–
1
votes
1
answer
56
ISI2018-DCG-10
Let $f’(x)=4x^3-3x^2+2x+k,$ $f(0)=1$ and $f(1)=4.$ Then $f(x)$ is equal to $4x^4-3x^3+2x^2+x+1$ $x^4-x^3+x^2+2x+1$ $x^4-x^3+x^2+2(x+1)$ none of these
Let $f’(x)=4x^3-3x^2+2x+k,$ $f(0)=1$ and $f(1)=4.$ Then $f(x)$ is equal to$4x^4-3x^3+2x^2+x+1$$x^4-x^3+x^2+2x+1$$x^4-x^3+x^2+2(x+1)$none of these
gatecse
391
views
gatecse
asked
Sep 18, 2019
Calculus
isi2018-dcg
calculus
differentiation
polynomials
+
–
0
votes
1
answer
57
ISI2018-DCG-24
Let $[x]$ denote the largest integer less than or equal to $x.$ The number of points in the open interval $(1,3)$ in which the function $f(x)=a^{[x^2]},a\gt1$ is not differentiable, is $0$ $3$ $5$ $7$
Let $[x]$ denote the largest integer less than or equal to $x.$ The number of points in the open interval $(1,3)$ in which the function $f(x)=a^{[x^2]},a\gt1$ is not diff...
gatecse
418
views
gatecse
asked
Sep 18, 2019
Calculus
isi2018-dcg
calculus
differentiation
+
–
0
votes
0
answers
58
ISI2018-DCG-29
Let $f(x)=(x-1)(x-2)(x-3)g(x); \: x\in \mathbb{R}$ where $g$ is twice differentiable function. Then there exists $y\in(1,3)$ such that $f’’(y)=0.$ there exists $y\in(1,2)$ such that $f’’(y)=0.$ there exists $y\in(2,3)$ such that $f’’(y)=0.$ none of the above is true.
Let $f(x)=(x-1)(x-2)(x-3)g(x); \: x\in \mathbb{R}$ where $g$ is twice differentiable function. Thenthere exists $y\in(1,3)$ such that $f’’(y)=0.$there exists $y\in(1,...
gatecse
358
views
gatecse
asked
Sep 18, 2019
Calculus
isi2018-dcg
calculus
differentiation
+
–
0
votes
1
answer
59
Gate 2002 - ME
Which of the following functions is not differentiable in the domain $[-1,1]$ ? (a) $f(x) = x^2$ (b) $f(x) = x-1$ (c) $f(x) = 2$ (d) $f(x) = Maximum (x,-x)$
Which of the following functions is not differentiable in the domain $[-1,1]$ ?(a) $f(x) = x^2$(b) $f(x) = x-1$(c) $f(x) = 2$(d) $f(x) = Maximum (x,-x)$
balchandar reddy san
2.7k
views
balchandar reddy san
asked
May 4, 2019
Calculus
engineering-mathematics
usergate2002
usermod
calculus
differentiation
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