A particle moves under the potential energy function V(x)=ax4−bx2, 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)}