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Let f(x) be differentiable for real x su...

Let `f(x)` be differentiable for real `x` such that `f^(prime)(x)>0on(-oo,-4),` `f^(prime)(x)<0on(-4,6),` `f^(prime)(x)>0on(6,oo),` If `g(x)=f(10-2x),` then the value of `g^(prime)(2)` is a. 1 b. 2 c. 0 d. 4

A

1

B

2

C

0

D

4

Text Solution

Verified by Experts

The correct Answer is:
C
`g(x)=f(10-2x)`
`rArr" "g'(x)=-2f'(10-2x)`
`rArr" "g'(2)=-2f'(6)`
Now f(x) is differentiable.
Also `f'(x) lt 0` on `(-4,6)`
and `f'(x) gt 0` on `(6,oo)`
`rArr" "f'6)=0`
`rArr" "g'(2)=0`
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