Let f(x) be a function that is defined for all real numbers. Which of the following is true?
a. If f'(c) is undefined, then x=c is a critical point of f(x).
b. If f(x) has a local minimum value at x=c, then f'(c)=0.
c. If f(x) is continuous on (a,b), then f(x) attains an absolute maximum value f(c) and an absolute minimum value f(d) for some numbers c and d in (a,b).
d. If f'(c)=0, then f(x) has a local maximum or minimum at x=c.
e. If f(x) has a critical point at x=c, then f'(c)=0.