Consider the function

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

Problem

f(x)=x^{4}+2x^{2}+5

. Which statement about its local extrema is correct? (a)

f

has two local minima at

x=-1

and

x=1

and a local maximum at

x=0

. (b)

f

has no critical points and hence no local extrema. (c)

f

has exactly one local minimum at

x=0

and no local maximum. (d)

f

has exactly one local maximum at

x=0