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if f(x) is a differentiable function whe...

if `f(x)` is a differentiable function wherever it is continuous and `f^(')(c_(1))=f^(')(c_(2))=0,f^(``)(c_(2))lt0`,
`f(c_(1))=5,f(c_(2))=0` and `(c_(1)gtc_(2))`
Now answer the following questions (1 to 2)
Q. if `f(x)` is continuous is `[c_(1),c_(2)]` & `f^(``)(c_(1)-f^(``)(c_(2))lt0`, then minimum number of roots of `f^(')(x)=0` in `[c_(1)-1,c_(2)+1]` is

A

2

B

3

C

4

D

5

Text Solution

Verified by Experts

The correct Answer is:
A, B
As `c_(2)` is local maximum and `c_(1)` is local minimum `impliesf(x)=0`
Has atleast two solution
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