1. Suppose that f is a differentiable function and f'(x) ≤ 4 on interval [-5, 2]. If f(2)= 6, then what is the smallest possible value that f(-5) could be? HINT: The mean value theorem.

3. ( interval (-2,6]. Here is the student's work: %3D A student used the Mean Value theorem on the function f(x) = |x - 1| on the (1) I calculated f(-2) = 3 and f(6) = 5. %3D (2) Then LO-[(-2) L(6)-f(-2) %3D %3D (3) By the Mean Value Theorem there is a number c in the interval (-2, 6] so that f'(c) = (The sentences have been numbered only to make it easier to refer to them.) For each sentence, explain why the student did that step. If there are any mistakes, tell the student what is incorrect about their work.

Find the number c that satisfes the conclusion of the Mean Value Theorem on the function f(x) = x³ on the interval [0, 4]. Write your answer correct to three decimals after the decimal point. Answer: