Let f (x) be a function that is differentiable everywhere and has a derivative f'(x) =...

Transcribed Image Text:

Let f (x) be a function that is differentiable everywhere and has a derivative f'(x) = 3x² + 14z + 6. Verify that the Intermediate Value Theorem for Derivatives applies to the function f'(x) on the interval [-6,-3], and find the value of c guaranteed by the theorem such that f'(c) = -2 If a function fis continuous, is the function / also differentiable? If not, give a counterexample. Explain your answer Let f (x) be a function that is differentiable everywhere and has a derivative f'(x) = 3x² + 14z + 6. Verify that the Intermediate Value Theorem for Derivatives applies to the function f'(x) on the interval [-6,-3], and find the value of c guaranteed by the theorem such that f'(c) = -2 If a function fis continuous, is the function / also differentiable? If not, give a counterexample. Explain your answer