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

HARD

JEE Main

IMPORTANT

Earn 100

Let a function $f : [0, 5] \to R$ be continuous, $f (1) = 3$ and $F$ be defined as: $F (x) = \int_{1}^{x} t^{2} g (t) d t,$ where $g (t) = \int_{1}^{t} f (u) d u .$ Then for the function $F (x),$ the point $x = 1$ 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 - 9th April 2019 Shift 1>Q 59

f (x)

is a non-zero polynomial of degree four, having local extreme points at

x = - 1, 0, 1;

then the set

S = {x \in R : f (x) = f (0)}

contains exactly

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 9th April 2019 Shift 1>Q 60

If the tangent to the curve,

y = x^{3} + a x - b

at the point

(1, - 5)

is perpendicular to the line,

- x + y + 4 = 0,

then which one of the following points lies on the curve?

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 9th April 2019 Shift 1>Q 61

Let

S

be the set of all values of

x

for which the tangent to the curve

y = f (x) = x^{3} - x^{2} - 2 x

(x, y)

is parallel to the line segment joining the points

(1, f (1))

and

(- 1, f (- 1)),

then

S

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 9th April 2019 Shift 2>Q 62

A water tank has the shape of an inverted right circular cone, whose semi-vertical angle is

{t a n}^{- 1} (\frac{1}{2}) .

Water is poured into it at a constant rate of

5 cubic m / \min .

Then the rate

(

m / \min),

at which the level of water is rising at the instant when the depth of water in the tank is

10 m;

is:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 9th January 2019 Shift 1>Q 63

The maximum volume

(in cubic m)

of the right circular cone having slant height

3 m

is:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 9th January 2019 Shift 1>Q 64

θ

denotes the acute angle between the curves,

y = 10 - x^{2}

and

y = 2 + x^{2}

at a point of their intersection, then

|\tan θ|

is equal to:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 8th April 2019 Shift 1>Q 65

S_{1}

and

S_{2}

are respectively the sets of local minimum and local maximum points of the function,

f (x) = 9 x^{4} + 12 x^{3} - 36 x^{2} + 25, x \in R,

then

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 8th April 2019 Shift 1>Q 66

If the tangents on the ellipse

4 x^{2} + y^{2} = 8

at the points

(1, 2)

and

(a, b)

are perpendicular to each other, then

a^{2}

is equal to

Let a function f:0,5→R be continuous, f1=3 and F be defined as: Fx=∫1xt2gtdt, where gt=∫1tfudu. Then for the function Fx, the point x=1 is:

Important Questions on Application of Derivatives

Learn and Prepare for any exam you want !

Let a function $f : [0, 5] \to R$ be continuous, $f (1) = 3$ and $F$ be defined as: $F (x) = \int_{1}^{x} t^{2} g (t) d t,$ where $g (t) = \int_{1}^{t} f (u) d u .$ Then for the function $F (x),$ the point $x = 1$ is: