Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-2>Q 59

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Let $f (x) = \frac{40}{3 x^{4} + 8 x^{3} - 18 x^{2} + 60}$ . Which of the following statement(s) about $f (x)$ is (are) correct ?

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Important Questions on Application of Derivatives

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-2>Q 60

A function

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

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-2>Q 66

Let

f (x), x \geq 0

be a non-negative continuous function and let

F (x) = \int_{0}^{x} f (t) d t, x \geq 0 .

If for some

c > 0, f (x) \leq c F (x)

for all

x \geq 0

, then

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-3>Q 1

The real number

k

for which the equation,

2 x^{3} + 3 x + k = 0

has two distinct real roots in

[0, 1] .

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-3>Q 3

For the function

f (x) = x \cos \frac{1}{x}, x \geq 1

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-3>Q 6

Let

f, g, h

be real valued functions defined on the interval

[0, 1]

by

f (x) = e^{x^{2}} + e^{- x^{2}}, g (x) = x e^{x^{2}} + e^{- x^{2}}

and

h (x) = x^{2} e^{x^{2}} + e^{- x^{2}}

. If

a, b

and

c

denote, respectively, the absolute maximum of

f, g

and

h

on

[0, 1]

, then

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-3>Q 11

The number of points in

(- \infty, \infty)

for which

x^{2} - xsinx - cosx = 0

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-3>Q 12

A rectangular sheet of fixed perimeter with sides having their lengths in the ratio

8 : 15

is converted into an open rectangular box by folding after removing squares of equal area from all four corners. If the total area of removed squares is

100,

the resulting box has maximum volume. The lengths of the sides of the rectangular sheet are

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-3>Q 14

The function

f (x) = 2 | x | + | x + 2 | - | | x + 2 | - 2 | x | |

has a local minimum or a local maximum at

x

equal to