Answer
a) $-2.5x^2+.5x^4$
b) $x=.7m,2m$
Work Step by Step
a) We know that the potential energy is equal to the negative integral of the force with respect to distance. Thus, it follows:
$U=\int(-5x+2x^3)dx=-2.5x^2+.5x^4$
b) The turning points will occur where U equals -1. Thus, we find:
$-1 = -2.5x^2 +.5x^4$
$x=.7m,2m$
