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The value of c in Rolle's theorem when f...

The value of c in Rolle's theorem when `f(x)=2x^(3)-5x^(2)-4x+3, x in [1//2,3]` is

A

2

B

`-(1)/(3)`

C

`-2`

D

`(2)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
A
Clearly, f(x) being a polynomial is continuous on [1/2,3] and differentiable on (1/2,3).
Also, `f((1)/(2))=f(3)=0`
So, by Rolle's theorem there exists ` c in (1//2,3)` such that
`f'(c)=0`
`rArr 6c^(2)-10c-4=0 " " [ :. f'(x) =6x^(2)-10x -4]`
`rArr 3c`
`rArr 3c^(2)-5c-2=0`
`rArr (c-2)(3c+1)=0 rArr c=2 in (1//2,3)`
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