EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Application of Derivatives>TS EAMCET 2021 (04-Aug Shift-1)>Q 13

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IMPORTANT

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The angle between the curves $2 x^{2} + y^{2} = 20$ and $4 y^{2} - x^{2} = 8$ at a point where they intersect in the $4^{th}$ quadrant is

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Important Questions on Application of Derivatives

EASY

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Application of Derivatives>TS EAMCET - 5 August 2021 Shift 1>Q 14

If the two curves

x = y^{2}

and

x y = k

cut each other at right angles, then a possible value of

k

is

EASY

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Application of Derivatives>TS EAMCET - 5 August 2021 Shift 2>Q 15

Let

R^{*} = R - \{(2 k - 1) \frac{π}{2} / k \in I\} .

The function

f : R^{*} \to R

is defined as

f (x) = \tan x - x,

then

f (x)

is

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Application of Derivatives>TS EAMCET 2020 (9-Sep Shift-1)>Q 16

The number of admissible values of

C

obtained when the Lagrange's mean value theorem is applied for the function

f (x) = x

on

[2, 5]

is

HARD

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Application of Derivatives>TS EAMCET 2018 (04-May Shift-1)>Q 17

Let

f (x)

be continuous on

[0, 6]

and differentiable on

(0, 6)

Let

f (0) = 12

and

f (6) = - 4

. If

g (x) = \frac{f (x)}{x + 1}

, then for some Lagrange's constant

c \in (0, 6), g^{'} (c) =

EASY

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Application of Derivatives>TS EAMCET - 5 August 2021 Shift 1>Q 18

The Rolle's theorem is not applicable to

f (x) = \{\begin{array}{cl} x, & 0 \leq x \leq 1 \\ 2 - x, & 1 \leq x \leq 2 \end{array}

on

[0, 2]

because

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Application of Derivatives>TS EAMCET 2020 (9-Sep Shift-1)>Q 19

The function

f (x) = x^{3} - 4 x^{2} + 4 x + 3

defined on

[- 1, 3]

has

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Application of Derivatives>TS EAMCET 2018 (04-May Shift-1)>Q 20

If

(α, β)

and

(γ, δ)

where

α < γ

are the turning points of

f (x) = 2 x^{3} - 15 x^{2} + 36 x - 8

, then

α - γ - β + δ =

HARD

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Application of Derivatives>TS EAMCET 2018 (04-May Shift-1)>Q 21

The height (in cm) of a cylinder of the greatest volume that can be inscribed in a sphere of radius

3 cm

, is