Answer:
[tex]F(x)=-3 N -(3N/m^2) x^2[/tex]
Explanation:
The force is equal to the negative of the derivative of the potential energy function:
[tex]F=-\frac{dU}{dx}[/tex]
In this problem, the potential energy function is
[tex]U(x)=3 x + 1 x^3[/tex]
Therefore, the force function is:
[tex]F(x)=-\frac{dU}{dx}=-\frac{d}{dx}(3x+1x^3)=-3-3x^2[/tex]
So, adding the units of measurement,
[tex]F(x)=-3 N -(3N/m^2) x^2[/tex]
