Please help, T/F

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) = ax² +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 , such that f(x) > f(a) for every x in (a- , a+ ).

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) =x³ 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-)*f"(a+) <0, for an arbitray positive number , then the function f(x) has an extreme value at x=a.

16.______If f'(a-)*f'(a+) <0, for an arbitray positive number , then the function f(x) has an extreme value at x=a whenever f'(a)=0, or f'(a) is undefined.

17.______The function y=(x-2)³ + 1 has an inflection point at (2, 1)

18. ______The function: is always increasing in (0, + ).

19.______If f'(a)=0, and f"(a)>0 then f has a minimum at x=a.

20.______If f"(x)>0 on an interval I then f(x) is increasing on I.