Consider the function
f(x) =(1 + x + x2 / 2! + x3 / 3! + . . . + xn / n! )e−x,
where n >= 4 is a positive integer. Which of the following statements
is correct?
(A) f has no local extremum
(B) For every n, f has a local maximum at x = 0
(C) f has no local extremum if n is odd and has a local maximum at
x = 0 when n is even
(D) f has no local extremum if n is even and has a local maximum at
x = 0 when n is odd.