True or False 1. If f'(x) =0 when x=c then f has either a minimum or maximum at x=C. 2. If a differentiable function f has a minimum or maximum at x=c, then f'(c)=0. 3. If f is continuous on an open interval (a, b) then the f attains maximum or minimum in (a, b). 4. If f'(x)=g'(x) then f(x) = g(x). 5. If x=c is an inflection point for f, then f (c) must be a maximum or minimum of f. 6. f(x) = ax? +bx +c, (with a = 0), can have only one critical point. 7. Second Shape Theorem includes the converse of First Shape Theorem. 8. If f(x) has a minimum at x=a, then there exists an s, such that f(x) > f(a) for every x in (a- E, at E ). 9. The mean value theorem applies as long as the function is continuous on an interval [a, b]. 10. If f (x) has an extreme value at x=a then f is differentiable at x=a. 11. If f(x) is continuous everywhere, and f(a)=f(b), then there exists x=c such that f'(c)=0. 12. if f(x) is continuous and differentiable everywhere, then f attains a max or min at x=a, if f'(a)=0. 13. The function f (x) =x" does not have an extreme value over the closed interval [a, b]. 14 If f(x) is not differentiable at x=a, then (a, f(a)) cannot be an extreme value of f. 15. If f"(a-e)*f"(ate) 0 then f has a minimum at x=a. 20. If f"(x)>0 on an interval I then f(x) is increasing on