MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 4 - Applications of Derivatives>Competitive Thinking>Q 99

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If $f (x) = x^{\frac{3}{2}} (3 x - 10), x \geq 0$ , then $f (x)$ is increasing in

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Important Questions on Applications of Derivatives

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IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 4 - Applications of Derivatives>Competitive Thinking>Q 100

The function

f (x) = \tan^{- 1} (\sin x + \cos x)

is an increasing function in

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 4 - Applications of Derivatives>Competitive Thinking>Q 101

Let $f (x) = \log (\sin x + \cos x), x \in (- \frac{π}{4}, \frac{3 π}{4})$ . Then find the interval in which $f$ is increasing

Note: Assume base of logarithm as $e$ everywhere.

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 4 - Applications of Derivatives>Competitive Thinking>Q 102

Let

f (x) = \int e^{x} (x - 1) (x - 2) d x

, then

f (x)

decreases in the interval

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IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 4 - Applications of Derivatives>Competitive Thinking>Q 103

If

f (x) = \frac{x}{\sin x}

and

g (x) = \frac{x}{\tan x}

, where

0 < x \leq 1

, then in this interval

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 4 - Applications of Derivatives>Competitive Thinking>Q 104

If

f (x) = \sin x - \cos x

, the function is decreasing in the interval, if

0 \leq x \leq 2 π

is

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MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 4 - Applications of Derivatives>Competitive Thinking>Q 105

Let

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

for every real number

x

. Then,

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 4 - Applications of Derivatives>Competitive Thinking>Q 106

The function

f (x) = {[x (x - 2)]}^{2}

is increasing in the set

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IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 4 - Applications of Derivatives>Competitive Thinking>Q 107

y = x {(x - 3)}^{2}

increases for all values of

x

lying in the interval.