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 86

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Function $f (x) = 2 x^{3} - 9 x^{2} + 12 x + 29$ is monotonically decreasing, when

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Important Questions on Applications of Derivatives

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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 87

The function

f (x) = x^{2} + 2 x - 5

is strictly increasing in the 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 88

The function

f (x) = x^{3} - 3 x^{2} - 24 x + 5

is an increasing function in the 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 89

For which interval the given function

f (x) = - 2 x^{3} - 9 x^{2} - 12 x + 1

is decreasing?

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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 90

Where does

f (x) = x + \sqrt{1 - x}, 0 < x < 1

decrease?

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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 91

The function

f (x) = \sin^{4} x + \cos^{4} x

increases, if

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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 92

The values of

{}^{'}a^{'}

for which the function

(a + 2) x^{3} - 3 a x^{2} + 9 a x - 1

decreases monotonically throughout for all real

x

, are

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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 93

If

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

is increasing function then the value of

x

lies 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 94

The function $f (x) = \log (1 + x) - \frac{2 x}{2 + x}$ is increasing on

Note: Assume base of logarithm as $e .$