Mathematics

Problem

The curve defined implicitly by

x^{4}-y=0

has a critical point at

(0,0)

. At that point

\dfrac{dy}{dx}=0

and

\dfrac{d^{2}y}{dx^{2}}=0

. Which statement best describes

(0,0)

? a)

(0,0)

is a saddle point because the second derivative is zero. b)

(0,0)

is a local minimum even though the second derivative test is inconclusive. c) No conclusion can be drawn about

(0,0)

; additional analysis cannot classify it. d)

(0,0)

is a local maximum because the second derivative is zero.