If `f(x)` is a differentiable function wherever it is continuous and `f'(c_1)=f'(c_2)=0` `f''(c_1).f''(c_2)<0, f(c_1)=5,f(c_2)=0` and `(c_1ltc_2)` . If `f(x) ` is continuous in `[c_1,c_2]` and `f''(c_1)-f''(c_2)>0` then minimum number of roots of `f'(x)=0` in `[c_1-1,c_2+1]` is

Options

A. 1
B. 2
C. 3
D. 4

Answer

B, C

Explanation

Here `c_(1)` is local maximum and `c_(2)` is local minimum `impliesf^(')(x)=0` has atleast two roots in `[c_(1)-1,c_(2)+1]`