Consider the following $U(x)$ graph. The function is $U(x)=-3x^3+18x^2-6x-14$ where $U(x)$ is in joules and $x$ is in meters. An object of mass $3\mathrm{.}21$ kg is released at $x=1\mathrm{.}0m$ with a velocity $6\mathrm{.}60\frac{m}{s}$ to the right.

A$.$ What is the total energy? $E=4\mathrm{.}0$

B$.$ What are the potential and kinetic energies at $x=3\mathrm{.}16m?$

$U=4\mathrm{.}0,K=4\mathrm{.}0$

C$.$ What is the object's velocity at $x=3\mathrm{.}16m?,v=4\mathrm{.}9V$

D$.$ What is the force on the object at $x=3\mathrm{.}16m?F=4\mathrm{.}9$

E$.$ Where are the points at which the force on the object is zero? $($List the smaller position first$)$

$x_1=4\mathrm{.}0,x_2=4\mathrm{.}0$

F$.$ For all $x$ shown on this graph, where is the velocity the greatest? $,x=4\mathrm{.}9$

G$.$ What is the magnitude of this maximum velocity? $,v=4\mathrm{.}0$

H$.$ For all $x$ shown on this graph, where is the velocity the least?

$x=4\mathrm{.}0$

I. What is the magnitude of this minimum velocity? $,v=4\mathrm{.}0$