A continous function y=f(x) crosses x-axis at points x=-3,0,2,5. Use mean value theorem to show that function has three critical points? I am stuck in this question kindly help
Actually, since f(x)=0 at all those points, we can use Rolle's Theorem, which is just a special case of the MVT were f(a) = f(b) on the interval [a,b].
Both theorems state that f'(c) exists with c in (a,b) such that the tangent is horizontal. That is, f'(c)=0, making it a critical point.
Three intervals, three critical points.