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JEE • MATHEMATICS • MAXIMA & MINIMA

Maxima & minima practice · Medium

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Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

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Showing 91-97 of 97 questions

91 Medium

91 of 97

Analyzing +4 | -1

Let

f\left( x \right) = {e^x}\sin x

, slope of the curve

y = f\left( x \right)

is maximum at

x = a

, if ‘a’ equals

View answer and explanation

Correct option: C

\frac{\pi }{2}

Option C (

\frac{\pi}{2}

) is correct because the slope's derivative is zero and its second derivative is negative at this point, indicating a maximum slope.

92 Medium

92 of 97

Application +4 | -1

The maximum value of xy subject to

x + y = 8

, is

View answer and explanation

Correct option: B

Option B (16) is correct because it represents the maximum value of xy when x + y = 8, found by optimization.

93 Medium

93 of 97

Analyzing +4 | -1

For

x \in\left(0, \frac{5 \pi}{2}\right)

, define

f(x)=\int_0^x \sqrt{t} \sin t d t

. Then

f

has

View answer and explanation

Correct option: C

local maximum at

\pi

and local minimum at

2 \pi

The function f(x) has a local maximum at

\pi

and a local minimum at

2\pi

because the sign of f'(x) changes from positive to negative at

\pi

and from negative to positive at

2\pi

94 Medium

94 of 97

Application +4 | -1

The minimum value of

2x + 3y

, when

xy = 6

, is

View answer and explanation

Correct option: A

Option A (12) is correct because the minimum value is found by differentiating the function and substituting the value of x.

95 Medium

95 of 97

Application +4 | -1

The maximum area of a triangle whose one vertex is at

(0,0)

and the other two vertices lie on the curve

y=-2 x^2+54

at points

(x, y)

and

(-x, y)

where

y > 0

, is :

View answer and explanation

Correct option: D

108

The correct answer is D (108) because the maximum area is found by expressing the area as a function of x, taking the derivative, and finding the critical points.

96 Medium

96 of 97

Application +4 | -1

A function

y=f(x)

has a second order derivative

f^{\prime \prime}(x)=6(x-1)

. If its graph passes through the point

(2,1)

and at that point the tangent to the graph is

y=3 x-5

, then the function is :

View answer and explanation

Correct option: B

(x-1)^{3}

Option B (

(x-1)^{3}

) is correct because integrating the second derivative and using the given conditions leads to this function.

97 Medium

97 of 97

Analyzing +4 | -1

The minimum value of

\left( {1 + \frac{1}{{{{\sin }^n}\alpha }}} \right)\left( {1 + \frac{1}{{{{\cos }^n}\alpha }}} \right)

, is

View answer and explanation

Correct option: C

{\left( {1 + {2^{n/2}}} \right)^2}

Option C is correct because the minimum value is found by setting the derivative equal to zero, solving for alpha, and substituting back into the original function.

Revision notes and key takeaways

Review MAXIMA & MINIMA in your textbook or class notes, then use this set to check your understanding.

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