Find the greatest and lowest value of $f(x,y) = e^{2xy}$ over the region R in the first quadrant enclosed by the lines $y = 4x$ and $x = 4y$ and the curves $xy = 2$ and $ xy = 7$.
Im guessing the lowest value must be when $x,y = 0.$ Since the region is so complex i don't know how to go about finding the maximum value.
No work necessary here - since $\exp(\cdot)$ is an increasing function, you are seeking to maximize and minimize $xy$ over the interval in question, to the minima of $e^4$ occur when $xy=2$ and the maxima of $e^{14}$ when $xy=7$.