Q.A particle which is constrained to move along the $x$-axis is subjected to a force in the same direction which varies with the distance $x$ of the particle from the origin as $F(x) = -kx + ax^3$. Here $k$ and $a$ are positive constants. For $x \geq 0$, the functional form of the potential energy $U(x)$ of the particle is one of four labelled curve sketches (a)-(d). (IIT 2002) [Figure only: the four options are graph shapes with no distinguishing printed text, so the correct graph cannot be identified from the extracted text alone.]