Answer
The Laplace's equation is satisfied.
Work Step by Step
We need to compute the Laplace's equation and prove that it equals to $0$.
In order to find the partial derivative we will differentiate, with respect to $x$, by keeping $y$ and $z$ as a constant, and vice versa:
$f_x=3 \implies f_{xx}=0$
and $f_y=2 \implies f_{yy}=0$
Consider the Laplace's equation $\nabla^2 f =\dfrac{\partial^2 f}{\partial x^2}+\dfrac{\partial^2 f}{\partial y^2}$
$\nabla^2 f =0+0=0$
Thus, the Laplace's equation is satisfied.
