1. True or False

1. True or False
a. _____ If f'(x) =0 at x=c then f has either a minimum or maximum at x=c.

b. _____ If a differentiable function f has a minimum or maximum at x=c, then f'(c)=0.

c. _____ If f is continuous in an open interval (a, b) then f attains maximum or minimum in (a, b).

d. _____ If f'(x)=g'(x) then f(x)=g(x) +c, where c is a constant.

e. _____ If x=c is an inflection point for f, then f(c) must be a local maximum or local minimum for f.

f. _____ f(x) = ax2 +bx +c, (with a ≠ 0), can have only one critical point.

g. _____ Second Shape Theorem is the converse of First Shape Theorem.

h. _____ 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).

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

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