A particle moves under the potential energy function

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

Problem

V(x)=a x^{4}-b x^{2}

, where

a

and

b

are positive constants. Which one of the following lists all equilibrium positions and correctly labels their stability? (a)

x=0

\;\text{(stable)},\;x=\pm\sqrt{b/2a}\;\text{(unstable)} (b)

x=0

\;\text{(unstable)},\;x=\pm\sqrt{b/2a}\;\text{(stable)} (c)

x=0

\;\text{(unstable)},\;x=\pm\sqrt{b/a}\;\text{(stable)} (d)

x=0

\;\text{only (stable)}