Let , where is a positive real number. Then, is a point…

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Let

f(x) = x^{n+1} + a \cdot x^n

, where

a

is a positive real number. Then,

x = 0

is a point of (1) local minimum for any integer

n

(2) local maximum for any integer

n

(3) local minimum if

n

is an even integer (4) local minimum if

n

is an odd integer