Search results for maxima-minima / GATE Overflow for GATE CSE

8 votes

2 answers

1

GATE CSE 2023 | Question: 18
Let $\qquad f(x)=x^{3}+15 x^{2}-33 x-36$ be a real-valued function. Which of the following statements is/are $\text{TRUE}?$ $f(x)$ does not have a local maximum. $f(x)$ has a local maximum. $f(x)$ does not have a local minimum. $f(x)$ has a local minimum.

Let $$\qquad f(x)=x^{3}+15 x^{2}-33 x-36$$be a real-valued function.Which of the following statements is/are $\text{TRUE}?$$f(x)$ does not have a local maximum.$f(x)$ has...

admin

5.3k views

admin asked Feb 15, 2023

36 votes

2 answers

2

GATE CSE 2008 | Question: 25
A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct extrema for the curve $3x^4-16x^3+24x^2+37$ is $0$ $1$ $2$ $3$

A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct extrema for the curve $3x^4-16x^3+24x^2+37$ is$0$$1$$2$$3...

Kathleen

8.5k views

Kathleen asked Sep 11, 2014

7 votes

2 answers

3

GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 11
Let $f(x)$ be a real-valued function all of whose derivatives exist. Recall that a point $x_0$ in the domain is called an inflection point of $f(x)$ if the second derivative $f^{\prime \prime}(x)$ changes sign at ... only inflection point. $x_0=0$ and $x_0=6$, both are inflection points. The function does not have an inflection point.

Let $f(x)$ be a real-valued function all of whose derivatives exist. Recall that a point $x_0$ in the domain is called an inflection point of $f(x)$ if the second derivat...

GO Classes

856 views

GO Classes asked Jan 28

3 votes

1 answer

4

GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 31
If $f, f^{\prime}$, and $f^{\prime \prime}$ are continuous and $f(2)=0, f^{\prime}(2)=2$, and $f^{\prime \prime}(2)=-3$, what can we say about the function $f(x)$ at $x=2?$ $f$ has a local minimum at $x=2$. $f$ has a local maximum at $x=2$. $f$ is increasing, at $x=2$ $f$ is decreasing, at $x=2$

If $f, f^{\prime}$, and $f^{\prime \prime}$ are continuous and $f(2)=0, f^{\prime}(2)=2$, and $f^{\prime \prime}(2)=-3$, what can we say about the function $f(x)$ at $x=2...

GO Classes

510 views

GO Classes asked Jan 13

0 votes

1 answer

5

Memory Based GATE DA 2024 | Question: 7
Consider the function $f(x) = \frac{1}{1+e^{-x}}$. Determine the derivative $f^{\prime}(x)$ when $f(x) = 0.4$.

Consider the function $f(x) = \frac{1}{1+e^{-x}}$. Determine the derivative $f^{\prime}(x)$ when $f(x) = 0.4$.

GO Classes

325 views

GO Classes asked Feb 4

1 votes

0 answers

6

Memory Based GATE DA 2024 | Question: 28
Consider a function $f$ with $f^1(X^*) = 0$ and $f^{1l}(X^*) > 0$. Based on these conditions, determine the nature of the critical point $X^*$ for the function $f(X)$. $X^*$ is a local maximum $X^*$ is a local minimum $X^*$ is a global maximum $X^*$ is a global minimum

Consider a function $f$ with $f^1(X^*) = 0$ and $f^{1l}(X^*) 0$. Based on these conditions, determine the nature of the critical point $X^*$ for the function \(f...

GO Classes

176 views

GO Classes asked Feb 4

0 votes

0 answers

7

Memory Based GATE DA 2024 | Question: 52
Consider the function $f(x) = \frac{x^4}{4} - \frac{2x^3}{3} - \frac{3x^2}{2}$. Which of the following statements about the critical points of $f(x)$ are correct? Local minima at $x = 0$ Local maxima at $x = 0$ Local minima at $x = 3$ Local minima at $x = -1$

Consider the function $f(x) = \frac{x^4}{4} - \frac{2x^3}{3} - \frac{3x^2}{2}$.Which of the following statements about the critical points of $f(x)$ are correct?Local...

GO Classes

168 views

GO Classes asked Feb 4

0 votes

0 answers

8

madeeasy
plz explain option c

plz explain option c

nihal_chourasiya

94 views

nihal_chourasiya asked Feb 1

3 votes

2 answers

9

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 $1$ $3$ $2$ $0$

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

385 views

GO Classes asked Aug 28, 2022

0 votes

2 answers

10

TIFR CSE 2022 | Part A | Question: 6
Let $f$ be a polynomial of degree $n \geq 3$ all of whose roots are non-positive real numbers. Suppose that $f(1)=1$. What is the maximum possible value of $f^{\prime}(1)?$ $1$ $n$ $n+1$ $\frac{n(n+1)}{2}$ $f^{\prime}(1)$ can be arbitrarily large given only the constraints in the question

Let $f$ be a polynomial of degree $n \geq 3$ all of whose roots are non-positive real numbers. Suppose that $f(1)=1$. What is the maximum possible value of $f^{\prime}(1)...

admin

701 views

admin asked Sep 1, 2022

7 votes

1 answer

11

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 $I$.

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

575 views

GO Classes asked Aug 28, 2022

3 votes

3 answers

12

GO Classes Test Series 2023 | Calculus | Test 1 | Question: 3
The function $f(x)=x^{4}-6 x^{2}$ is increasing on the intervals $(0, \sqrt{3})$ only $(\sqrt{3}, \infty)$ only $(-\infty,-\sqrt{3})$ and $(0, \sqrt{3})$ only $(-\sqrt{3}, 0)$ and $(\sqrt{3}, \infty)$ only

The function $f(x)=x^{4}-6 x^{2}$ is increasing on the intervals$(0, \sqrt{3})$ only$(\sqrt{3}, \infty)$ only$(-\infty,-\sqrt{3})$ and $(0, \sqrt{3})$ only$(-\sqrt{3}, 0)...

GO Classes

635 views

GO Classes asked Aug 28, 2022

8 votes

2 answers

13

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

1.0k views

GO Classes asked Aug 28, 2022

2 votes

0 answers

14

GO Classes 2023 | IIITH Mock Test 1 | Question: 62
The expression $\dfrac{(x+y) - |x-y|}{2}$ is equal to : The maximum of $x$ and $y$ The minimum of $x$ and $y$ $1$ None of the above

The expression $\dfrac{(x+y) - |x-y|}{2}$ is equal to :The maximum of $x$ and $y$The minimum of $x$ and $y$$1$None of the above

GO Classes

634 views

GO Classes asked Mar 26, 2023

23 votes

3 answers

15

GATE CSE 2020 | Question: 1
Consider the functions $e^{-x}$ $x^{2}-\sin x$ $\sqrt{x^{3}+1}$ Which of the above functions is/are increasing everywhere in $[ 0,1]$? Ⅲ only Ⅱ only Ⅱ and Ⅲ only Ⅰ and Ⅲ only

Consider the functions $e^{-x}$$x^{2}-\sin x$$\sqrt{x^{3}+1}$Which of the above functions is/are increasing everywhere in $[ 0,1]$?Ⅲ onlyⅡ onlyⅡ and Ⅲ onlyⅠ a...

Arjun

12.3k views

Arjun asked Feb 12, 2020

15 votes

2 answers

16

GATE CSE 1987 | Question: 1-xxvi
If $f(x_{i}).f(x_{i+1})< 0$ then There must be a root of $f(x)$ between $x_i$ and $x_{i+1}$ There need not be a root of $f(x)$ between $x_{i}$ and $x_{i+1}$ There fourth derivative of $f(x)$ with respect to $x$ vanishes at $x_{i}$ The fourth derivative of $f(x)$ with respect to $x$ vanishes at $x_{i+1}$

If $f(x_{i}).f(x_{i+1})< 0$ thenThere must be a root of $f(x)$ between $x_i$ and $x_{i+1}$There need not be a root of $f(x)$ between $x_{i}$ and $x_{i+1}$There fourth der...

makhdoom ghaya

2.8k views

makhdoom ghaya asked Nov 9, 2016

0 votes

2 answers

17

GATE CSE 2023 | Memory Based Question: 11
Let $f(x)=x^3+15 x^2-33 x-36$ be a real valued function. Which statement is/are TRUE? $f(x)$ has a local maximum. $f(x)$ does NOT have a local maximum. $f(x)$ has a local minimum. $f(x)$ does NOT have a local minimum.

Let $f(x)=x^3+15 x^2-33 x-36$ be a real valued function. Which statement is/are TRUE?$f(x)$ has a local maximum.$f(x)$ does NOT have a local maximum.$f(x)$ has a local mi...

GO Classes

4.0k views

GO Classes asked Feb 5, 2023

8 votes

1 answer

18

GO Classes Test Series 2023 | Calculus | Test 1 | Question: 19
The equation $x^{5}+x+1=0$ has a solution in the interval $[0,1]$ $[-1,0]$ $[-2,-1]$ $[1,2]$

The equation $x^{5}+x+1=0$ has a solution in the interval$[0,1]$$[-1,0]$$[-2,-1]$$[1,2]$

GO Classes

527 views

GO Classes asked Aug 28, 2022

6 votes

1 answer

19

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...

GO Classes

667 views

GO Classes asked Aug 28, 2022

6 votes

1 answer

20

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 $f(6) \geq 8$ $f(6)<8$ $f(6)<5$ $f(6)=5$

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

458 views

GO Classes asked Aug 28, 2022

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