For each statement below indicate whether it is true or false, if it is true, give a brief explanation why it is true If false, give a value of from the graph of f(x) over the interval [0,4] above that provides a counterexample to the statement.

a. If x = c is a local extremum of f(x), then x = c is a critical point of f(x).

b. If f’(c) = 0 then c is either a local minimum or a local maximum of f(x).

c. If f’(c) does not exist then r is either a local minimum or a local maximum of f(x).

d. The absolute extrema of f (x) on an interval [a, b] are always at one end of the interval, x = a or x = b.