Rolle's Theorem Function

Question

Find all numbers, $c$ that satisfies the conclusion of Rolle's Theorem for the following function,

$f(x)=x^2−10x+10,[0,10]$

I haven't learned this theorem yet and am confused on what to do.

Answer 1

Notice that first it must hold:$$f(0)=f(10)$$which is true. The next step is $$f'(c)=2c-10=0$$which leaves us with one option $c=5$. A sketch would be like this:https://www.desmos.com/calculator/ewss4auny0