There is a clever proof of the Mean Value Theorem from Rolle's Theorem. The idea is to

Question:

There is a clever proof of the Mean Value Theorem from Rolle's Theorem. The idea is to tilt the function f so that it takes on the same values at the endpoints a and b. In particular, we apply Rolle's Theorem to the function

For the following functions, show that g(a) = g(b), apply Rolle's Theorem to g, and find the derivative of f at a point where g'(x) = 0.
23. f(x) = x2, a = l, and b = 2.
24. In general, without assuming a particular form for f(x) or values for a and b.