Mathematics

Problem

The function

f(x)=x^{3}+3p x^{2}+3x

depends on the real parameter

p

. For which of the following ranges of

p

does the function possess at least one local maximum? a)

p < -1 \text{ or } p > 1

p \le -1 \text{ or } p \ge 1

p > 1

only d)

-1 < p < 1