# MATH110/April 2017/Question 11 (a)

Hi Aili,

I think what you used is not the mean value theorem, but the intermediate value theorem. When you use it, it would be great if you mention that the function f' satisfies the assumption of the theorem. i.e., the continuity of the function. Also, in the definition of the critical value c, we also have one more condition that f' changes its sign around c. So, please add explanation on this part, too. Thanks!

Umm, I have made some changes to my solutions. I am not sure about where I should put "in the definition of the critical value c, we also have one more condition that f' changes its sign around c"... but I did verify the assumptions of IVT.

Sorry, Aili. I don't think we need to add that part. I was confused about the definition. What you did is enough.

Thanks for revising the solution!