Sounds like the Mean Value Theorem
Let a; b be real numbers such that 0 < a < b. Let f be a function continuous on [a, b]
and diferentiable on (a, b). Assume that f satises the property
f(a) = f(b) = 0 and f'(a) = 0:
Show that there exist c in (a; b) such that the tangent to f at c passes through 0.
Any help? I am totaly lost.