Using the following theorem, prove these estimates, on the given interval.
(a) e^x > a+x+((x^2)/2) for x on the interval (0,1]; find a quadratic upper estimate
(b) ln(1+x) > x-x^2 for x on the interval [0,1]; find a quadratic upper estimate
The theorem states: Suppose f ''(x) exists in an interval I containing a. Then for each x in I, there is a point c lying between a and x such that f(x) = f(a)+f '(a)(x-a)+(f ''(c)/2)(x-a)^2.