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Let $f (x)$ be a twice differentiable function for all real values of $x$ and satisfies $f (1) = 1, f (2) = 4, f (3) = 9 .$

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Important Questions on Application of Derivatives

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KVPY Aptitude Test - Stream SX

IMPORTANT

Practice Book for KVPY Aptitude Test - Stream SX Mathematics>Chapter 6 - Application of Derivatives>EXERCISE>Q 21

In which of the following functions is Rolle's theorem applicable?

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Practice Book for KVPY Aptitude Test - Stream SX Mathematics>Chapter 6 - Application of Derivatives>EXERCISE>Q 22

If there is an error of

k %

in measuring the edge of a cube, then the percent error in estimating its volume is

HARD

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IMPORTANT

Practice Book for KVPY Aptitude Test - Stream SX Mathematics>Chapter 6 - Application of Derivatives>EXERCISE>Q 23

A man is moving away from a tower

41.6 m

high at a rate of

2 m / s

. If the eye level of the man is

1.6 m

above the ground, then the rate at which the angle of elevation of the top of the tower changes, when he is at a distance of

30 m

from the foot of the tower, is

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Practice Book for KVPY Aptitude Test - Stream SX Mathematics>Chapter 6 - Application of Derivatives>EXERCISE>Q 24

Suppose that

f

is differentiable for all

x

and that

f^{'} (x) \leq 2

for all

x .

f (1) = 2

and

f (4) = 8,

then

f (2)

has the value equal to

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IMPORTANT

Practice Book for KVPY Aptitude Test - Stream SX Mathematics>Chapter 6 - Application of Derivatives>EXERCISE>Q 25

The radius of a right circular cylinder increases at the rate of

0.1 cm / \min,

and the height decreases at the rate of

0.2 cm / \min .

The rate of change of the volume of the cylinder, in

{cm}^{3} / \min .

, when the radius is

2 cm

and the height is

3 cm

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Practice Book for KVPY Aptitude Test - Stream SX Mathematics>Chapter 6 - Application of Derivatives>EXERCISE>Q 26

A cube of ice melts without changing its shape at the uniform rate of

4 {cm}^{3} / \min .

The rate of change of the surface area of the cube, in

{cm}^{2} / \min,

when the volume of the cube is

125 {cm}^{3},

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Practice Book for KVPY Aptitude Test - Stream SX Mathematics>Chapter 6 - Application of Derivatives>EXERCISE>Q 27

Let

f^{'} (x) = e^{x^{2}}

and

f (0) = 10 .

A < f (1) < B

can be concluded from the mean value theorem, then the largest value of

(A - B)

equals

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IMPORTANT

Practice Book for KVPY Aptitude Test - Stream SX Mathematics>Chapter 6 - Application of Derivatives>EXERCISE>Q 28

f

be a continuous function on

[0, 1],

differentiable in

(0, 1)

such that

f (1) = 0,

then there exists some

c \in (0, 1)

such that

Let fx be a twice differentiable function for all real values of x and satisfies f(1)=1, f(2)=4, f(3)=9.

Important Questions on Application of Derivatives

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Let $f (x)$ be a twice differentiable function for all real values of $x$ and satisfies $f (1) = 1, f (2) = 4, f (3) = 9 .$