The Level Curves of a Function $f ( x , y )$

Essay

The level curves of a function $f ( x , y )$ and a curve with equation $g ( x , y ) = c$ ( $C$ constant) are given below. Estimate the point where $f$ has a maximum value and the point where $f$ has a minimum value, subject to the constraint that $g ( x , y ) = c$ . Indicate your answer in the figure.