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Recent questions tagged differentiation
3
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1
answer
31
GO Classes Test Series 2023 | 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
408
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goclasses2024-calculus-1
goclasses
calculus
differentiation
1-mark
7
votes
1
answer
32
GO Classes Test Series 2023 | 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
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in
Calculus
Aug 28, 2022
by
GO Classes
560
views
goclasses2024-calculus-1
goclasses
calculus
differentiation
maxima-minima
multiple-selects
2-marks
8
votes
1
answer
33
GO Classes Test Series 2023 | 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
asked
in
Calculus
Aug 28, 2022
by
GO Classes
573
views
goclasses2024-calculus-1
goclasses
calculus
differentiation
maxima-minima
multiple-selects
2-marks
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 $g(c)=1$ $g^{\prime}(c)=1$ $g(c)=0$ $g^{\prime}(c)=0$
GO Classes
asked
in
Calculus
Aug 28, 2022
by
GO Classes
632
views
goclasses2024-calculus-1
goclasses
calculus
differentiation
maxima-minima
2-marks
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 $f(0)$. $-337 / 6$ $-74 / 3$ $23 / 9$ $37 / 4$
GO Classes
asked
in
Calculus
Aug 28, 2022
by
GO Classes
534
views
goclasses2024-calculus-1
goclasses
calculus
differentiation
2-marks
4
votes
1
answer
36
GO Classes Test Series 2023 | 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
497
views
goclasses2024-calculus-1
goclasses
calculus
differentiation
maxima-minima
2-marks
3
votes
1
answer
37
GO Classes Test Series 2023 | 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
333
views
goclasses2024-calculus-1
goclasses
calculus
differentiation
maxima-minima
2-marks
6
votes
1
answer
38
GO Classes Test Series 2023 | 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
asked
in
Calculus
Aug 28, 2022
by
GO Classes
433
views
goclasses2024-calculus-1
goclasses
calculus
differentiation
maxima-minima
2-marks
8
votes
1
answer
39
GO Classes Test Series 2023 | 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
505
views
goclasses2024-calculus-1
goclasses
calculus
differentiation
maxima-minima
2-marks
0
votes
0
answers
40
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
makhdoom ghaya
asked
in
Study Resources
Aug 15, 2022
by
makhdoom ghaya
155
views
missing-videos
free-videos
video-links
go-classroom
differentiation
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, ${f}'(x)$.
kidussss
asked
in
Calculus
Jul 8, 2022
by
kidussss
317
views
calculus
differentiation
0
votes
3
answers
42
Applied Mathematics Question
Let $f(x) = e^{x^2},$ then find $f''(x).$
kidussss
asked
in
Calculus
Jul 7, 2022
by
kidussss
454
views
calculus
differentiation
0
votes
0
answers
43
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 $x=\frac{\pi }{2}.$
soujanyareddy13
asked
in
Others
Aug 30, 2020
by
soujanyareddy13
174
views
tifrmaths2016
differentiation
calculus
2
votes
1
answer
44
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
Arjun
asked
in
Calculus
Sep 23, 2019
by
Arjun
546
views
isi2014-dcg
calculus
differentiation
0
votes
2
answers
45
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
Arjun
asked
in
Calculus
Sep 23, 2019
by
Arjun
715
views
isi2014-dcg
calculus
continuity
differentiation
0
votes
1
answer
46
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 $- \frac{24}{5} \bigg[ \frac{1}{(x-1)^5} - \frac{48}{(2x+3)^5} \bigg]$ ... $\frac{64}{5} \bigg[ \frac{1}{(x-1)^5} + \frac{48}{(2x+3)^5} \bigg]$
Arjun
asked
in
Others
Sep 23, 2019
by
Arjun
680
views
isi2014-dcg
calculus
differentiation
functions
0
votes
2
answers
47
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 $x=2$
Arjun
asked
in
Calculus
Sep 23, 2019
by
Arjun
818
views
isi2015-mma
calculus
continuity
differentiation
definite-integral
non-gate
0
votes
1
answer
48
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
Arjun
asked
in
Calculus
Sep 23, 2019
by
Arjun
477
views
isi2015-mma
calculus
differentiation
0
votes
1
answer
49
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 $\mid \alpha \mid <1$ $\alpha >1$ $\alpha < -1$
Arjun
asked
in
Calculus
Sep 23, 2019
by
Arjun
471
views
isi2015-mma
calculus
limits
differentiation
0
votes
1
answer
50
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 $x$ $f(1) \leq g(1)$ $f(1) \geq g(1)$
Arjun
asked
in
Calculus
Sep 23, 2019
by
Arjun
415
views
isi2015-mma
calculus
differentiation
0
votes
2
answers
51
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
gatecse
asked
in
Calculus
Sep 18, 2019
by
gatecse
425
views
isi2015-dcg
calculus
continuity
differentiation
0
votes
0
answers
52
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.
gatecse
asked
in
Calculus
Sep 18, 2019
by
gatecse
368
views
isi2016-dcg
calculus
continuity
differentiation
functions
1
vote
2
answers
53
ISI2017-DCG-30
If $f(x)=e^{5x}$ and $h(x)=f’’(x)+2f’(x)+f(x)+2$ then $h(0)$ equals $38$ $8$ $4$ $0$
gatecse
asked
in
Calculus
Sep 18, 2019
by
gatecse
328
views
isi2017-dcg
calculus
differentiation
functions
2
votes
1
answer
54
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 $0$ $2017$ $2018$ $2019$
gatecse
asked
in
Calculus
Sep 18, 2019
by
gatecse
646
views
isi2018-dcg
calculus
functions
differentiation
1
vote
1
answer
55
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
gatecse
asked
in
Calculus
Sep 18, 2019
by
gatecse
372
views
isi2018-dcg
calculus
differentiation
polynomials
0
votes
1
answer
56
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 $0$ $3$ $5$ $7$
gatecse
asked
in
Calculus
Sep 18, 2019
by
gatecse
389
views
isi2018-dcg
calculus
differentiation
0
votes
0
answers
57
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.
gatecse
asked
in
Calculus
Sep 18, 2019
by
gatecse
344
views
isi2018-dcg
calculus
differentiation
0
votes
1
answer
58
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) $f(x) = Maximum (x,-x)$
balchandar reddy san
asked
in
Calculus
May 4, 2019
by
balchandar reddy san
2.6k
views
engineering-mathematics
usergate2002
usermod
calculus
differentiation
1
vote
1
answer
59
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
Applied Course
asked
in
Calculus
Jan 16, 2019
by
Applied Course
668
views
applied-course-2019-mock1
calculus
differentiation
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