Find c in (a, b) so tangent passes through 0

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 satises 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.

Sounds like the Mean Value Theorem

hmm or could it be Rolles Theorem...
Anyon else?

When you wrote , was that supposed to be

If you meant , then it is Mean Value.

It is just different to see since that doesn't come up in either theorem.

No it is actually f'(a)...
That is why I am getting confused. I have never seen that before

The tangent line is .
To pass through (0,0) we must have .
Consider the function apply Rolle's Theorem.

is x = a?

Suppose that then .
Moreover, on so if then .