Find $\displaystyle a,b,c$ constants so that the directional derivative of $\displaystyle f(x,y,z)=axy^2+byz+cz^2x^3$ on $\displaystyle (1,2,-1)$ has a maximum value of $\displaystyle 64$ on a parallel direction to the $\displaystyle z$ axis.

I think we can calculate the directional derivative by using $\displaystyle \langle\nabla f(x_0),x_0\rangle$ where $\displaystyle x_0=(1,2,-1),$ but a maximum value is asked which I don't get, and I don't either get when it says "on a parallel direction to the $\displaystyle z.$"