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

If the surface area of a cube is increasing at a rate of $3.6 {cm}^{2} / \sec$ , retaining its shape; then the rate of change of its volume (in ${cm}^{3} / \sec$ ), when the length of a side of the cube is $10 cm$ , is:

90% studentsanswered this correctly

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 - 3 September 2020 Shift 2>Q 44

If the tangent to the curve

y = e^{x}

at a point

(c, e^{c})

and the normal to the parabola

y^{2} = 4 x

at the point

(1, 2)

intersect at the same point on the

x -

axis, then the value of

c

is .....

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 4 September 2020 Shift 2>Q 45

The area (in sq. units) of the largest rectangle $A B C D$ whose vertices $A$ and $B$ lie on the $x$ -axis and vertices $C$ and $D$ lie on the parabola, $y = x^{2} - 1$ below the $x$ -axis, is :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 5 September 2020 Shift 2>Q 46

x = 1

is a critical point of the function

f (x) = (3 x^{2} + a x - 2 - a) e^{x},

then

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 5 September 2020 Shift 2>Q 47

Which of the following points lies on the tangent to the curve

x^{4} e^{y} + 2 \sqrt{y + 1} = 3

at the point

(1, 0)

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 5 September 2020 Shift 2>Q 48

If the lines

x + y = a

and

x - y = b

touch the curve

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

at the points where the curve intersects the

x -

axis, then

\frac{a}{b}

is equal to

\dots

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 6 September 2020 Shift 1>Q 49

The position of a moving car at time

t

is given by

f (t) = a t^{2} + b t + c, t > 0

, where

a, b and c

are real numbers greater than

1

. Then the average speed of the car over the time interval

[t_{1}, t_{2}]

is attained at the point:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 6 September 2020 Shift 1>Q 50

Let

A D

and

B C

be two vertical poles at

A and B

respectively on a horizontal ground. If

A D = 8 m

BC = 11 m

AB = 10 m;

then the distance (in meters) of a point

M

lying in between

AB

from the point

A

such that

{MD}^{2} + {MC}^{2}

is minimums, is__

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 6 September 2020 Shift 2>Q 51

The set of all real values

λ

for which the function

f (x) = (1 - \cos^{2} x) . (λ + \sin x), x \in (- \frac{π}{2}, \frac{π}{2})

, has exactly one maxima and exactly one minima, is :

If the surface area of a cube is increasing at a rate of 3.6cm2/sec, retaining its shape; then the rate of change of its volume (in cm3/sec), when the length of a side of the cube is 10cm, is:

Important Questions on Application of Derivatives

Learn and Prepare for any exam you want !

If the surface area of a cube is increasing at a rate of $3.6 {cm}^{2} / \sec$ , retaining its shape; then the rate of change of its volume (in ${cm}^{3} / \sec$ ), when the length of a side of the cube is $10 cm$ , is: