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Recent questions tagged differentiation
3
votes
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GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 37
Which of the following is/are TRUE? There is a differentiable function $f(x)$ with the property that $f(1)=-2$ and $f(5)=14$ and $f^{\prime}(x)\lt 3$ for every real number $x$. There exists a function $f$ ... $a\lt c\lt b$ and $f(c)=0$. If $f$ is differentiable at the number $x$, then it is continuous at $x$.
Which of the following is/are TRUE?There is a differentiable function $f(x)$ with the property that $f(1)=-2$ and $f(5)=14$ and $f^{\prime}(x)\lt 3$ for every real number...
GO Classes
611
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GO Classes
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Jan 21
Calculus
goclasses2024-mockgate-12
goclasses
calculus
differentiation
multiple-selects
2-marks
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3
votes
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.
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 $f^{\prime}(1)=0$. T...
admin
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admin
asked
Mar 14, 2023
Calculus
tifr2023
calculus
differentiation
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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 $c(t)$ ... $\frac{1}{2 \pi}$ $2 \pi$ $\sqrt{3} \pi$ $\frac{1}{\sqrt{3} \pi}$ $1$
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 $...
admin
321
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admin
asked
Sep 1, 2022
Calculus
tifr2022
calculus
differentiation
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8
votes
2
answers
4
GO Classes Test Series 2023 | 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
Which of the following functions satisfy the conditions of Rolle's Theorem on the interval $[-1,1]?$ $$\begin{aligned}&f(x)=1-x^{2 / 3}\\&g(x)=x^{3}-2 x^{2}-x+2\\&h(x)=\c...
GO Classes
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GO Classes
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Aug 28, 2022
Calculus
goclasses2024-calculus-1
goclasses
calculus
differentiation
maxima-minima
1-mark
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4
votes
1
answer
5
GO Classes Test Series 2023 | Calculus | Test 1 | Question: 6
Suppose that the derivative of a function $h$ is given by: $ h^{\prime}(x)=x(x-1)^{2}(x-2) $ On what interval(s) is $h$ increasing? $(-\infty, 0)$ $(-\infty, 0)$ and $(2, \infty)$ $(0,2)$ $(0,1)$ and $(2, \infty)$
Suppose that the derivative of a function $h$ is given by:$$h^{\prime}(x)=x(x-1)^{2}(x-2)$$On what interval(s) is $h$ increasing?$(-\infty, 0)$$(-\infty, 0)$ and $(2, \in...
GO Classes
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GO Classes
asked
Aug 28, 2022
Calculus
goclasses2024-calculus-1
goclasses
calculus
differentiation
1-mark
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7
votes
3
answers
6
GO Classes Test Series 2023 | 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
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...
GO Classes
782
views
GO Classes
asked
Aug 28, 2022
Calculus
goclasses2024-calculus-1
goclasses
calculus
differentiation
multiple-selects
1-mark
+
–
7
votes
2
answers
7
GO Classes Test Series 2023 | 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.
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
897
views
GO Classes
asked
Aug 28, 2022
Calculus
goclasses2024-calculus-1
goclasses
calculus
differentiation
multiple-selects
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