Chapter 12.2, Problem 45E

Approximate mountains Suppose the elevation of Earth’s surface over a 16-mi by 16-mi region is approximated by the function

$z=10e^{-\left(x^2+y^2\right)}+5e^{-\left({\left(x+5\right)}^2+{\left(y-3\right)}^2\right)/10}+4e^{-2\left({\left(x-4\right)}^2+{\left(y+1\right)}^2\right)}.$

a.    Graph the height function using the window [–8, 8] × [–8, 8] × [0, 15].

b.    Approximate the points (x, y) where the peaks in the landscape appear.

c.    What are the approximate elevations of the peaks?