EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Application of Derivatives>WBJEE 2019>Q 15

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Let $f : [1, 3] \to R$ be a continuous function that is differentiable in $(1, 3)$ an $f^{'} (x) = | f (x) |^{2} + 4$ for all $x \in (1, 3) .$ Then

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Important Questions on Application of Derivatives

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Application of Derivatives>WBJEE 2018>Q 16

Let

f : [a, b] \to R

be differentiable on

[a, b]

and

k \in R .

Let

f (a) = 0 = f (b) .

Also let

J (x) = f^{'} (x) + k f (x) .

Then

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Application of Derivatives>WBJEE 2018>Q 17

Let

f : [a, b] \to R

be such that

f

is differentiable in

(a, b), f

is continuous at

x = a

and

x = b

and moreover

f (a) = 0 = f (b) .

Then

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Application of Derivatives>WBJEE 2018>Q 18

Let

f : R \to R

be a twice continuously differentiable function such that

f (0) = f (1) = f^{'} (0) = 0

. Then

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Application of Derivatives>WBJEE 2020>Q 19

Let

f (x) = 1 - \sqrt{(x^{2})},

where the square root is to be taken positive, then

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Application of Derivatives>WBJEE 2020>Q 20

If the function

f (x) = 2 x^{3} - 9 a x^{2} + 12 a^{2} x + 1

,

(a > 0)

attains its maximum and minimum at

p

and

q

respectively such that

p^{2} = q,

then

a

is