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

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).