Let f x = 2 x + tan - 1 x and g x = log e 1 + x 2 + x , x ∈ 0 , 3 . Then

There exists x ∈ 0 , 3 such that f ' x < g ' x

There exist 0 < x 1 < x 2 < 3 such that f x < g x , ∀ x ∈ x 1 , x 2

MEDIUM

JEE Main

IMPORTANT

Earn 100

Let $f (x) = \{\begin{matrix} x^{3} - x^{2} + 10 x - 7, & x \leq 1 \\ - 2 x + \log_{2} (b^{2} - 4), & x > 1 \end{matrix}$ Then the set of all values of $b$ , for which $f (x)$ has maximum value at $x = 1$ , is:

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Important Questions on Application of Derivatives

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 26 July 2022 Shift 1>Q 130

The number of distinct real roots of the equation

x^{5} (x^{3} - x^{2} - x + 1) + x (3 x^{3} - 4 x^{2} - 2 x + 4) - 1 = 0

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 26 July 2022 Shift 2>Q 131

If the maximum value of

a

, for which the function

f_{a} (x) = \tan^{- 1} 2 x - 3 a x + 7

is non-decreasing in

(- \frac{π}{6}, \frac{π}{6})

, is

\bar{a}

, then

f_{\bar{a}} (\frac{π}{8})

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 27 July 2022 Shift 1>Q 132

Let

M

and

N

be the number of points on the curve

y^{5} - 9 x y + 2 x = 0

, where the tangents to the curve are parallel to

x

-axis and

y

-axis, respectively. Then the value of

M + N

equals _______.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 27 July 2022 Shift 2>Q 133

A water tank has the shape of a right circular cone with axis vertical and vertex downwards. Its semivertical angle is

\tan^{- 1} \frac{3}{4}

. Water is poured in it at a constant rate of

6

cubic meter per hour. The rate (in square meter per hour), at which the wet curved surface area of the tank is increasing, when the depth of water in the tank is

4

meters, is _______.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 28 July 2022 Shift 2>Q 134

The function

f (x) = x e^{x (1 - x)}, x \in R

, is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 28 July 2022 Shift 2>Q 135

The sum of the absolute maximum and absolute minimum values of the function

f (x) = \tan^{- 1} (\sin x - \cos x)

in the interval

[0, π]

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 29 July 2022 Shift 1>Q 136

Let $f (x) = 3^{{(x^{2} - 2)}^{3} + 4}, x \in R$ . Then which of the following statements are true?

$P : x = 0$ is a point of local minima of $f$

$Q : x = \sqrt{2}$ is a point of inflection of $f$

$R : f^{'}$ is increasing for $x > \sqrt{2}$

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 29 July 2022 Shift 2>Q 137

If the tangent to the curve

y = x^{3} - x^{2} + x

at the point

(a, b)

is also tangent to the curve

y = 5 x^{2} + 2 x - 25

at the point

(2, - 1)

, then

|2 a + 9 b|

is equal to ______.

Let fx=x3-x2+10x-7,x≤1-2x+log2b2-4,x>1 Then the set of all values of b, for which fx has maximum value at x=1, is:

Important Questions on Application of Derivatives

Learn and Prepare for any exam you want !

Let $f (x) = \{\begin{matrix} x^{3} - x^{2} + 10 x - 7, & x \leq 1 \\ - 2 x + \log_{2} (b^{2} - 4), & x > 1 \end{matrix}$ Then the set of all values of $b$ , for which $f (x)$ has maximum value at $x = 1$ , is: