The potential energy function (in J ) of a particle in a region of space is given as U = 2 x 2 + 3 y 3 + 2 z…

Given $U=2x^2+3y^3+2z$

The expression for the $x-$component of the force can be calculated as follows: 

$\begin{array}{rcl}{F}_x& =& -\frac{\partial U}{\partial x}\\ & =& -4x\end{array}$

Hence, at the point $\left(1, 2, 3\right) \mathrm{m}$, the value of the force is given by

$\begin{array}{rcl}\left|F_x\right|& =& \left|-4\times 1\right| \mathrm{N}\\ & =& 4 \mathrm{N}\end{array}$