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Let f(x)=(x-7)^2 (x-2)^7, x in [2,7]. th...

Let `f(x)=(x-7)^2 (x-2)^7, x in [2,7].` the value of `theta in (2,7)` such that `f'(theta)=0` is equal to

A

`48/4`

B

`53/9`

C

`53/7`

D

`49/9`

Text Solution

Verified by Experts

The correct Answer is:
B
Given ` f ( x ) = ( x - 7 ) ^ 2 ( x - 2 ) ^ 7 `
` rArr f ( theta ) = ( theta - 7 ) ^ 2 ( theta - 2 ) ^ 7 `
On differentiating w.r.t ` theta `, we get
` rArr f' ( theta ) = 2 ( theta - 7 ) ( theta -2 ) ^ 7 + 7 ( theta - 2 ) ^6 ( theta - 7 ) ^ 2 `
Put ` f' ( theta ) = 0 `
` rArr ( theta -7 ) ( theta - 2 ) ^ 6[ 2 ( theta - 2 ) + 7 ( theta - 7 ) ] = 0 `
` rArr 9 theta = 53 rArr theta = (53 ) /(9 ) `
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-PRACTICE SET 15-PAPER 2 (MATHEMATICS)
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  13. int(0)^(pi)(1)/(1+sin x)dx is equal to

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  20. Equation cos 2x+7=a(2-sin x) can have a real solution for

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