Assume that f is non-negative on (0,1)

1. Jan 14, 2006

mansi

Hello...I need help and I know this is a very simple problem...I don't know why I'm getting stuck( Maybe because it's past midnight here )

Assume that f is non-negative on (0,1) and the third derivative of f exists on (0,1).If f(x)=0 for at least 2 values of x in (0,1), show that there exists "c" in (0,1) such that the third derivative of f at c is 0.

this is what i've done...let a,b be the points where f vanishes. that is f(a)=f(b)=0
so we can use Rolle's theorem and get a point p such that f^(p)=0.

What next??

2. Jan 14, 2006

matt grime

draw a picture: hint it is non-negative and touches the x-axis twice (necessarily at local minima)