(A) Find the Number C Whose Existence Is Guaranteed by the Mean

Short Answer

(a) Find the number c whose existence is guaranteed by the Mean Value Theorem for Integrals for the function f on [a, b], and (b) sketch the graph of f on [a, b] and the rectangle with base on [a, b] that has the same area as that of the region under the graph of
f. $f(x)$ = $\frac{1}{2}$ $x^{2}$ + x; [0, 1]