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

MEDIUM

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IMPORTANT

Earn 100

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

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Important Questions on Application of Derivatives

HARD

TS EAMCET

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

MEDIUM

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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

MEDIUM

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Application of Derivatives>TS EAMCET 2019 (03-May Shift-2)>Q 22

A right solid circular cylinder of given volume will have the least total surface area when

EASY

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Application of Derivatives>TS EAMCET 2019 (03-May Shift-2)>Q 23

The smaller side of the rectangle with the largest area, that can be inscribed inside a semi-circle of radius

2

units is of length

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Application of Derivatives>TS EAMCET 2019 (03-May Shift-2)>Q 24

Let

f (x) = (x - 3)^{2018} (x - 2)^{2019}, x \in ℝ

. If

f (α)

is a relative maximum of

f

at

x = α

, then

2 α + 3 f (α) =