Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-2>Q 45

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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 46

If

f (x) = 2 x + \cot^{- 1} x + \ln (\sqrt{1 + x^{2}} - x)

, then

f (x) :

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-2>Q 47

Let

g (x) = 2 f (\frac{x}{2}) + f (1 - x)

and

f^{''} (x) < 0

in

0 \leq x \leq 1

, then

g (x)

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-2>Q 48

Let

f (x) = x^{\frac{m}{n}}

for

x \in R

where

m

and

n

are integers,

m

even and

n

odd and

0 < m < n

. Then

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-2>Q 49

Let

f

and

g

be two differentiable functions defined on an interval I such that

f (x) \geq 0

and

g (x) \leq 0

for all

x \in I

and

f

is strictly decreasing on

I

while

g

is strictly increasing on

I

then

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-2>Q 50

Let

ϕ (x) = {(f (x))}^{3} - 3 {(f (x))}^{2} + 4 f (x) + 5 x + 3 \sin x + 4 \cos x \forall x \in R

, where

f (x)

is a differentiable function

\forall x \in R

, then

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-2>Q 51

If

p, q and r

be real, then the intervals in which,

f (x) = |\begin{matrix} x + p^{2} & p q & p r \\ p q & x + q^{2} & q r \\ p r & q r & x + r^{2} \end{matrix}|

.

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-2>Q 52

If

f (x) = \frac{x^{2}}{2 - 2 \cos x}; g (x) = \frac{x^{2}}{6 x - 6 \sin x}

where

0 < x < 1

, then

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-2>Q 53

Let

f (x) = \frac{x}{\sin x}, x \in (0, \frac{π}{2})

. Then the interval in which at least one root of the equation lie

\frac{2}{x - f (\frac{π}{12})} + \frac{3}{x - f (\frac{π}{4})} + \frac{4}{x - f (\frac{5 π}{12})} = 0

.