How Can You Sketch the Potential of a Particle in Vector Calculus?

[implet]

Homework Statement

"A particle at position {\mathbf r} experiences a force (ar^{-3}+br^{-4}){\mathbf r}. Sketch the potential as a function of r in the different cases that arise according to the signs of a and b."

Homework Equations

-\nabla {\mathbf V} = {\mathbf F}

The Attempt at a Solution

I just can't see where to start with this one. I haven't done much vector calculus...

Many thanks :)

 

[CompuChip]

Actually,
-\mathbf{\nabla} V = {\mathbf F}
because V is not really a vector.

Anyway, you need a function V_n whose gradient looks like
\nabla V_n = \frac{\mathbf{r}}{r^n},
right?

My hint to you is: try differentiating
\frac{1}{r^{n - 1}}
with respect to x, y and z and see what you get.