Let f x = x cos - 1 ⁡ - sin ⁡ x , x ∈ - π 2 , π 2 , then which of the following is true?

f ' is decreasing in - π 2 , 0 and increasing in 0 , π 2

f ' is increasing in - π 2 , 0 and decreasing in 0 , π 2

f is not differentiable at x = 0

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

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:

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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 - 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 :

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 52

If the tangent to the curve,

y = f (x) = x \log_{e} x, (x > 0)

at a point

(c, f (c))

is parallel to the line-segment joining the points

(1, 0)

and

(e, e)

,then

c

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 8th January 2020 Shift 1>Q 53

Let

f (x) = x \cos^{- 1} (- \sin |x|), x \in [- \frac{π}{2}, \frac{π}{2}],

then which of the following is true?

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 8th January 2020 Shift 1>Q 54

Let the normal at a point

P

on the curve

y^{2} - 3 x^{2} + y + 10 = 0

intersect the

y

-axis at

(0, \frac{3}{2}) .

m

is the slope of the tangent at

P

to the curve, then

|m|

is equal to ___________.

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 8th January 2020 Shift 2>Q 55

The length of the perpendicular from the origin, on normal to the curve,

x^{2} + 2 x y - 3 y^{2} = 0

, at the point

(2, 2)

, is.

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 8th January 2020 Shift 2>Q 56

Let

f (x)

be a polynomial of degree

3

, such that

f (- 1) = 10, f (1) = - 6, f (x)

has a critical point at

x = - 1

and

f' (x)

has a critical point at

x = 1 .

Then

f (x)

has local minima at

x =

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 9th January 2020 Shift 1>Q 57

A spherical iron ball of

10 c m

radius is coated with a layer of ice of uniform thickness that melts at a rate of

50 {c m}^{3} / m i n

. When the thickness of ice is

5 c m

, then the rate (in

c m / m i n

.) at which the thickness of ice decreases, is:

The position of a moving car at time t is given by f(t)=at2+bt+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 t1,t2 is attained at the point:

Important Questions on Application of Derivatives

Learn and Prepare for any exam you want !

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: