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Recent questions tagged differentiation
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GO Classes 2023 | IIITH Mock Test 3 | Question: 42
If $y=\dfrac{4 x-5}{x+5},$ then $\dfrac{d y}{d x}$ equals $\frac{20}{(x+5)^2}$ $\frac{25}{(x+5)^2}$ $\frac{x+5}{4 x-5}$ $4$
GO Classes
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Calculus
Apr 15
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GO Classes
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2
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1
answer
2
TIFR CSE 2023 | Part A | Question: 14
Let $f(x)=a x^{3}+b x^{2}+c x+d$ be a polynomial, where $a, b, c, d$ are unknown real numbers. It is further given that $f(1)=1, f(2)=2, f(3)=9$, and $f^{\prime}(1)=0$. Then, the value of $f^{\prime}(2)$ must be $1$ $2$ $3$ $4$ $f^{\prime}(2)$ cannot be determined uniquely from the information given in the question.
admin
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in
Calculus
Mar 14
by
admin
109
views
tifr2023
calculus
differentiation
0
votes
0
answers
3
TIFR CSE 2022 | Part A | Question: 14
Suppose $w(t)=4 e^{i t}, x(t)=3 e^{i(t+\pi / 3)}, y(t)=3 e^{i(t-\pi / 3)}$ and $z(t)=3 e^{i(t+\pi)}$ are points that move in the complex plane as the time $t$ varies in $(-\infty, \infty)$. Let $c(t)$ ... $\frac{1}{2 \pi}$ $2 \pi$ $\sqrt{3} \pi$ $\frac{1}{\sqrt{3} \pi}$ $1$
Lakshman Bhaiya
asked
in
Calculus
Sep 1, 2022
by
Lakshman Bhaiya
139
views
tifr2022
calculus
differentiation
6
votes
2
answers
4
GO Classes Test Series 2024 | Calculus | Test 1 | Question: 5
Which of the following functions satisfy the conditions of Rolle's Theorem on the interval $[-1,1]?$ $ \begin{aligned} &f(x)=1-x^{2 / 3}\\ &g(x)=x^{3}-2 x^{2}-x+2\\ &h(x)=\cos \left(\frac{\pi}{4}(x+1)\right) \end{aligned} $ Rolle's Theorem applies to: both $f$ and $g$ both $g$ and $h$ $g$ only $h$ only
GO Classes
asked
in
Calculus
Aug 28, 2022
by
GO Classes
205
views
goclasses2024-calculus-1
goclasses
calculus
differentiation
maxima-minima
1-mark
3
votes
1
answer
5
GO Classes Test Series 2024 | Calculus | Test 1 | Question: 6
Suppose that the derivative of a function $h$ is given by: $ h^{\prime}(x)=x(x-1)^{2}(x-2) $ On what interval(s) is $h$ increasing? $(-\infty, 0)$ $(-\infty, 0)$ and $(2, \infty)$ $(0,2)$ $(0,1)$ and $(2, \infty)$
GO Classes
asked
in
Calculus
Aug 28, 2022
by
GO Classes
90
views
goclasses2024-calculus-1
goclasses
calculus
differentiation
1-mark
4
votes
2
answers
6
GO Classes Test Series 2024 | Calculus | Test 1 | Question: 7
Let $q(x)$ be a continuous function which is defined for all real numbers. A portion of the graph of $q^{\prime}(x)$, the derivative of $q(x)$, is shown below. On which of the following interval(s) is $q(x)$ increasing? $(0,2)$ $(2,4)$ $(7,9)$ None of these
GO Classes
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in
Calculus
Aug 28, 2022
by
GO Classes
152
views
goclasses2024-calculus-1
goclasses
calculus
differentiation
multiple-selects
1-mark
4
votes
2
answers
7
GO Classes Test Series 2024 | Calculus | Test 1 | 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 $1$ is a ... at $1 .$ If $f^{\prime \prime}(0)0$ then there is a point in $(0,1)$, where $f$ has an inflection point.
GO Classes
asked
in
Calculus
Aug 28, 2022
by
GO Classes
168
views
goclasses2024-calculus-1
goclasses
calculus
differentiation
multiple-selects
1-mark
2
votes
1
answer
8
GO Classes Test Series 2024 | Calculus | Test 1 | Question: 9
Evaluate $y^{\prime \prime}(1)$ where $y=e^{x}+x^{e}$. $0$ $1$ $e^{2}$ $e$
GO Classes
asked
in
Calculus
Aug 28, 2022
by
GO Classes
74
views
goclasses2024-calculus-1
goclasses
calculus
differentiation
1-mark
3
votes
0
answers
9
GO Classes Test Series 2024 | Calculus | Test 1 | 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 $r$ such that $f(x)=r$ ... decreasing on $I$. If $f^{\prime}(x)>0$ for all $x \in I$, then $f(x)$ is strictly decreasing on $I$.
GO Classes
asked
in
Calculus
Aug 28, 2022
by
GO Classes
88
views
goclasses2024-calculus-1
goclasses
calculus
differentiation
maxima-minima
multiple-selects
2-marks
5
votes
1
answer
10
GO Classes Test Series 2024 | Calculus | Test 1 | 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 $3$ and $5 .$ ... $h(x)$ is a continuous function and $h(1)=4$ and $h(2)=5$, then $h(x)$ has no roots between $1$ and $2.$
GO Classes
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in
Calculus
Aug 28, 2022
by
GO Classes
114
views
goclasses2024-calculus-1
goclasses
calculus
differentiation
maxima-minima
multiple-selects
2-marks
3
votes
1
answer
11
GO Classes Test Series 2024 | Calculus | Test 1 | 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 $g(c)=1$ $g^{\prime}(c)=1$ $g(c)=0$ $g^{\prime}(c)=0$
GO Classes
asked
in
Calculus
Aug 28, 2022
by
GO Classes
121
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goclasses2024-calculus-1
goclasses
calculus
differentiation
maxima-minima
2-marks
3
votes
1
answer
12
GO Classes Test Series 2024 | Calculus | Test 1 | 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 $f(0)$. $-337 / 6$ $-74 / 3$ $23 / 9$ $37 / 4$
GO Classes
asked
in
Calculus
Aug 28, 2022
by
GO Classes
114
views
goclasses2024-calculus-1
goclasses
calculus
differentiation
2-marks
2
votes
1
answer
13
GO Classes Test Series 2024 | Calculus | Test 1 | Question: 16
The sum of three positive numbers is $12$ and two of them are equal. Find the largest possible product. $86$ $64$ $48$ $72$
GO Classes
asked
in
Calculus
Aug 28, 2022
by
GO Classes
97
views
goclasses2024-calculus-1
goclasses
calculus
differentiation
maxima-minima
2-marks
3
votes
1
answer
14
GO Classes Test Series 2024 | Calculus | Test 1 | Question: 17
If $f(x)=e^{x} g(x), g(0)=2$ and $g^{\prime}(0)=1$, then $f^{\prime}(0)$ is $1$ $3$ $2$ $0$
GO Classes
asked
in
Calculus
Aug 28, 2022
by
GO Classes
58
views
goclasses2024-calculus-1
goclasses
calculus
differentiation
maxima-minima
2-marks
4
votes
1
answer
15
GO Classes Test Series 2024 | Calculus | Test 1 | 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 $f(6) \geq 8$ $f(6)<8$ $f(6)<5$ $f(6)=5$
GO Classes
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in
Calculus
Aug 28, 2022
by
GO Classes
82
views
goclasses2024-calculus-1
goclasses
calculus
differentiation
maxima-minima
2-marks
4
votes
1
answer
16
GO Classes Test Series 2024 | Calculus | Test 1 | Question: 19
The equation $x^{5}+x+1=0$ has a solution in the interval $[0,1]$ $[-1,0]$ $[-2,-1]$ $[1,2]$
GO Classes
asked
in
Calculus
Aug 28, 2022
by
GO Classes
100
views
goclasses2024-calculus-1
goclasses
calculus
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2-marks
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Recent questions tagged differentiation
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This story is same like my tier 3 college btech...
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You can attempt now:...
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