Solve the Problem $\left( x _ { 0 } , y _ { 0 } , z _ { 0 } \right)$

Essay

Solve the problem.
-Consider a small region inside an elastic material such as gelatin. As the material "jiggles", this small region oscillates about its equilibrium position $\left( x _ { 0 } , y _ { 0 } , z _ { 0 } \right)$ . The force that tends to restore the small region to its equilibrium position can be approximated as $F = - k \left( x - x _ { 0 } \right) i - k \left( y - y _ { 0 } \right) \mathbf { j } - k ( z - z 0 ) \mathbf { k }$ Find a potential function $f$ for this force field.