Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>Assignment>Q 41

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Maximum area of a rectangle which can be inscribed in a circle of a given radius $R$ is

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Important Questions on Application of Derivatives

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Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>Assignment>Q 42

If atmosphere pressure at a height of

h

units is given by the function

P (h) = h e^{- h}

then pressure is maximum at the height of

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Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>Assignment>Q 43

The radius of cylinder of maximum volume which can be inscribed in a right circular cone of radius

R

and height

H

(axis of cylinder and cone are same)

H

given by

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Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>Assignment>Q 44

Let

f (x) = \{\begin{cases} - |x - 2|; x \leq 3 \\ x^{2} - 2 x - 4; x > 3 \end{cases}

Then the number of critical points on the graph of the function is

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Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>Assignment>Q 45

The least area of a circle circumscribing any right triangle of area

S

is

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Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>Assignment>Q 46

If

f (x) = x {(1 - x)}^{3}

then which of following is true?

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Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>Assignment>Q 47

The cost function at American Gadget is

C (x) = x^{3} - 6 x^{2} + 15 x

(

x

is thousands of units and

x > 0

). The production level at which average cost is minima is

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Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>Assignment>Q 48

Let

f (x) = a x^{2} - b |x|

, where

a

and

b

are constant. Then at

x = 0

,

f (x)

has

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Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>Assignment>Q 49

The maximum value of

{(\frac{1}{x})}^{2 x^{2}}

is -