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X X Let f(t) = 4t - 16 and consider the two area functions A(x) = f(t) dt and F(x) = f(t) dt. Complete parts (a) (c). 4 ( lype an expression using x as the variable.) c. Show that A(x) - F(x) is a constant and that A'(x) = F'(x) =f(x). First prove A(x) - F(x) is a constant. Using the expressions for A(x) and F(x) found in previous steps, subtract F(x) from A(X). The value of A(x) - F(x) is 18 . (Simplify your answer.) Now prove that A'(x) = F'(x) = f(x). Using the expressions for A(x) and F(x) found in previous steps, take the derivative of A(x) and F(x) respectively and compare the results. A'(X) = (Simplify your answer. Do not factor.) F' (X) = (Simplify your answer. Do not factor.) Recall that f(t) = 4t - 16, substitute x for t to get f(x). f(x) = (Simplify your answer. Do not factor.) Thus, A'(x) = F'(x) =f(x). X