Consider the Mean Value Theorem:

If f is a continuous function on the closed interval [a,b], and differentiable on the open interval

(a,b), then there exists at least one point c (a,b) such that .

For the following functions, find c satisfying the Mean Value Theorem for f(x) on the interval [0,1] when

f(x) = ex f(x) = x2 f(x) = 1/(x + 1).