Mean Value Theorem for quadratic functions Consider the quadratic function f(x) = Ax +Bx+C where A, B, and C are real numbers with A ? 0. Show that when the Mean Value Theorem is applied to f on the interval [a, b], the number c guaranteed by the theorem is the midpoint of the interval.

Solution 33AE Step 1 In this problem we have to apply mean value theorem to quadratic function. First let us see the statement of mean value theorem Mean Value theorem: If f is defined and continuous on the closed interval [a,b]and differentiable on the open interval (a,b)then there is at least one point cin (a,b)that is f(b) f(a) a < c < bsuch that f(c) = ba