I have answered the questions below:

Let f (x) be a function that is differentiable everywhere and has a derivative f' (x) = 3x2 + 14x + 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 (4 points) B I UIf a function fis continuous, is the function f also differentiable? If not, give a counterexample. Explain your answer. (4 points) B I y VxLet, food be a funetim differentiable everywhere with derivative f () = gx 2 + 14x + 8 so the function will be - FC = 3x + tutor+ c where c is am integrating constant using , first we will show that Intermediate, value theorem holds for film) - 6,-37 As f'cos is a polynomial so all the conditions of Intermediate value theorem are satisfied. I'mmy is differentiable on ( - 6 , -3 ) firms is continuous on [- 6,-37 f' ( - 8 ) = 3. ( - 1 ) + 14 . ( 8 ) +6 and - 246 1 ( - 3 ) - a . ( - 3 ) + 14 . ( - 3 ) + 6 = 45 let , 45 CK