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.

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.