Let f : 0 , 2 → R be a twice differentiable function such that f ' ' x > 0 , for all x ∈ 0 , 2 . If ϕ x = f x + f 2 – x , then ϕ is

decreasing on 0,1 and increasing on ( 1,2 )

increasing on ( 0,1 ) and decreasing on 1,2

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 $θ$ 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:

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Important Questions on Application of Derivatives

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

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 8th April 2019 Shift 1>Q 67

Let

f : [0, 2] \to R

be a twice differentiable function such that

f^{''} (x) > 0,

for all

x \in [0, 2] .

ϕ (x) = f (x) + f (2 - x),

then

ϕ

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 8th April 2019 Shift 2>Q 68

The height of a right circular cylinder of maximum volume inscribed in a sphere of radius

3

is:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 10th April 2019 Shift 1>Q 69

Let

f (x) = e^{x} - x

and

g (x) = x^{2} - x, \forall x ϵ R

. Then the set of all

x ϵ R

, where the function

h (x) = (f o g) (x)

is increasing, is:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 10th April 2019 Shift 2>Q 70

If the tangent to the curve

y = \frac{x}{x^{2} - 3}, x \in R, (x \neq \pm \sqrt{3}),

at a point

(α, β) \neq (0, 0)

on it is parallel to the line

2 x + 6 y - 11 = 0,

then:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 10th April 2019 Shift 2>Q 71

A spherical iron ball of radius

10 c m

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 the ice is

5 c m,

then the rate at which the thickness

(

c m / m i n)

of the ice decreases, is :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 10th January 2019 Shift 2>Q 72

A helicopter is flying along the curve given by

y - x^{\frac{3}{2}} = 7, (x \geq 0) .

A soldier positioned at the point

(\frac{1}{2}, 7)

, who wants to shoot down the helicopter when it is nearest to him. Then this nearest distance is:

If θ denotes the acute angle between the curves, y=10-x2 and y=2+x2 at a point of their intersection, then tan⁡θ is equal to:

Important Questions on Application of Derivatives

Learn and Prepare for any exam you want !

If $θ$ 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: