# Please help, T/F1. _____ 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^{2} +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 ε, such that f(x) > f(a) for every x in (a- ε, a+ ε).

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^{3} 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-ε)*f"(a+ε) <0, for an arbitray positive number ε, then the function f(x) has an extreme value at x=a.

16. ______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 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.

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