3 At what po?ints c? does the conclusion of the Mean Value Theorem hold ? f?or?? ) = x on the interval [?10,10]?

Solution 6E Step 1 In this problem we have to find the value of c for which the conclusion of the mean value theorem for f(x) = x holds on the interval [-10,10] 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 Step 2 3 Given that f(x) = x is defined on [-10,10] Since f is a polynomial, f is continuous and differentiable everywhere. Hence f is continuous in the closed interval [-10,10] and differentiable in the open interval (-10,10). Thus f satisfies all the conditions of mean value theorem on the given interval [-10,10]. Therefore by Mean value theorem, there is at least one point cin (-10,10) such f(10) f(10) that f(c) = 10+10 … ( 1)