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Recent questions tagged differentiation

6 votes
1 answer
34
GO Classes Test Series 2023 | 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 $g(c)=1$ $g^{\prime}(c)=1$ $g(c)=0$ $g^{\prime}(c)=0$
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$$g^{\p...
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6 votes
1 answer
35
GO Classes Test Series 2023 | Calculus | Test 1 | Question: 15
Suppose $f$ is twice differentiable with $ f^{\prime \prime}(x)=7 x-2, \quad f^{\prime}(-2)=0, \quad \text { and } \quad f(-2)=-2 . $ Find $f(0)$. $-337 / 6$ $-74 / 3$ $23 / 9$ $37 / 4$
Suppose $f$ is twice differentiable with$$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$$23 / 9...
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0 votes
1 answer
41
Applied Mathematics Derivative
Please find derivation of the following equation. Let $f(x)=e^{x^{2}}\ln x,$ then find, ${f}'(x)$.
Please find derivation of the following equation.Let $f(x)=e^{x^{2}}\ln x,$ then find, ${f}'(x)$.
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0 votes
3 answers
42
Applied Mathematics Question
Let $f(x) = e^{x^2},$ then find $f''(x).$
Let $f(x) = e^{x^2},$ then find $f''(x).$
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1 votes
2 answers
43
GATE Overflow Test Series | Calculus | Test 1 | Question: 1
If $f(x) = x^{100} + x^{99}+ \dots + x + 1$ then $f'(1)$ is equal to $5050$ $5049$ $5051$ none of the above
If $f(x) = x^{100} + x^{99}+ \dots + x + 1$ then $f'(1)$ is equal to$5050$$5049$$5051$none of the above
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2 votes
1 answer
45
ISI2014-DCG-13
Let the function $f(x)$ be defined as $f(x)=\mid x-1 \mid + \mid x-2 \:\mid$. Then which of the following statements is true? $f(x)$ is differentiable at $x=1$ $f(x)$ is differentiable at $x=2$ $f(x)$ is differentiable at $x=1$ but not at $x=2$ none of the above
Let the function $f(x)$ be defined as $f(x)=\mid x-1 \mid + \mid x-2 \:\mid$. Then which of the following statements is true?$f(x)$ is differentiable at $x=1$$f(x)$ is di...
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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$$f(x)$ is differentiable at $x=0$, and $f’(0) \neq 0$...
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0 votes
1 answer
47
ISI2014-DCG-49
Let $f(x) = \dfrac{x}{(x-1)(2x+3)}$, where $x>1$. Then the $4^{th}$ derivative of $f, \: f^{(4)} (x)$ is equal to $- \frac{24}{5} \bigg[ \frac{1}{(x-1)^5} - \frac{48}{(2x+3)^5} \bigg]$ ... $\frac{64}{5} \bigg[ \frac{1}{(x-1)^5} + \frac{48}{(2x+3)^5} \bigg]$
Let $f(x) = \dfrac{x}{(x-1)(2x+3)}$, where $x>1$. Then the $4^{th}$ derivative of $f, \: f^{(4)} (x)$ is equal to$- \frac{24}{5} \bigg[ \frac{1}{(x-1)^5} – \frac{48}{(2...
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0 votes
1 answer
49
ISI2015-MMA-72
The map $f(x) = a_0 \cos \mid x \mid +a_1 \sin \mid x \mid +a_2 \mid x \mid ^3$ is differentiable at $x=0$ if and only if $a_1=0$ and $a_2=0$ $a_0=0$ and $a_1=0$ $a_1=0$ $a_0, a_1, a_2$ can take any real value
The map $f(x) = a_0 \cos \mid x \mid +a_1 \sin \mid x \mid +a_2 \mid x \mid ^3$ is differentiable at $x=0$ if and only if$a_1=0$ and $a_2=0$$a_0=0$ and $a_1=0$$a_1=0$$a_0...
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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$\alpha$...
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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)...
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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...
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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...
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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$$0$
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2 votes
1 answer
55
ISI2018-DCG-9
Let $f(x)=1+x+\dfrac{x^2}{2}+\dfrac{x^3}{3}...+\dfrac{x^{2018}}{2018}.$ Then $f’(1)$ is equal to $0$ $2017$ $2018$ $2019$
Let $f(x)=1+x+\dfrac{x^2}{2}+\dfrac{x^3}{3}...+\dfrac{x^{2018}}{2018}.$ Then $f’(1)$ is equal to $0$$2017$$2018$$2019$
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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
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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...
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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,...
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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) $f(x) = Maximum (x,-x)$
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1 votes
1 answer
60
Applied Course | Mock GATE | Test 1 | Question: 11
The value of derivative of $f(x) = \mid x -1 \mid + \mid x -3 \mid \text{ at } x = 2$ is $-2$ $0$ $2$ Not defined
The value of derivative of $f(x) = \mid x -1 \mid + \mid x -3 \mid \text{ at } x = 2$ is$-2$$0$$2$Not defined
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