True 1. _____ Second Shape Theorem includes the converse of First Shape Theorem

True 1. _____ Second Shape Theorem includes the converse of First Shape Theorem.
or False (Optional Explanation)

2. _____ If f(x) has a minimum at x=a, then there exists an ε, such that f(x) > f(a) for every x in (a- ε, a+ ε).

3. _____ The mean value theorem applies as long as the function is continuous on an interval [a, b].

4. _____ If f (x) has an extreme value at x=a then f is differentiable at x=a.

5. ______If f(x) is continuous everywhere, and f(a)=f(b), then there exists x=c such that f'(c)=0.

6. ______ if f(x) is continuous and differentiable everywhere, then f attains a max or min at x=a, if f'(a)=0.

7. ______The function f (x) =x3 does not have an extreme value over the closed interval [a, b].

8. ______If f(x) is not differentiable at x=a, then (a, f(a)) cannot be an extreme value of f.

9. ______If f”(a-ε)*f”(a+ε) <0, for an arbitray positive number ε, then the function f(x) has an extreme value at x=a.

10. ______If f'(a-ε)*f'(a+ε) 0 then f has a minimum at x=a.

14. ______If f”(x)>0 on an interval I then f(x) is increasing on I.