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Let f(x) lt 0 AA x in (-oo, 0) and f (x)...

Let `f(x) lt 0 AA x in (-oo, 0) and f (x) gt 0 ,AA x in (0,oo) ` also `f (0)=0,` Again `f'(x) lt 0 ,AA x in (-oo, -1) and f '(x) gt 0, AA x in (-1,oo)` also `f '(-1)=0` given `lim _(x to -oo) f (x)=0 and lim _(x to oo) f (x)=oo` and function is twice differentiable.
If `f'(x) lt 0 AA x in (0,oo)and f'(0)=1` then number of solutions of equation `f (x)=x ^(2)` is : (a) 1 (b) 2 (c) 3 (d) 4

A

2

B

3

C

4

D

None of these

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The correct Answer is:
D
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