Answer
$$
\begin{array}{l}
\nabla g=\left\langle g_x, g_y\right\rangle \\
g_x=y^2 \text { and } g_y=2 x y \text { so } \nabla_g=\left\langle y^2, 2 x y\right\rangle
\end{array}
$$
$$
\text { point }(2,1) \quad x=2 \quad y=1 \text { so } \nabla g=\langle 1,4\rangle
$$
Work Step by Step
$$
Question \ says \ g(x,y)= xy^{2} \\
At \ point (2,-1) \
g(2,-1) =2 \\ so\\ xy^{2} =2\\
\text{
let's leave x alone to draw} \\
\text {the graph of level curce easily: }\\
x= \frac{2}{y^2}\\
\text{
Thus we can sketch gradient vector}\\
\text{ at initial point (2,-1) on the level curve}
$$
