Question

Find the critical point(s) of the function.
Then use the second derivative test to classify the nature of each point, if possible.
Finally, determine the relative extrema of the function

f(x,y)= 3x^2 - 3e^5y^2

Answer 1

There is a lot of work to this problem, so I'll talk you through the steps, but the work must be done by yourself
first you need to find derivatives of fx and fy and then find when they go to zero. Once you figure out what those values you are for fxx and fyy, youll want to plug those values back into the original equation in order to find the z value. Then, youll want to figure out fxx and fyy to "test to classify the nature of each point."
After all that work is said and done,
d=fxx*fyy-fxy^2
if d is less than 0 than its a saddle point
if fxx<o and d>0 its a maxima
if fxx>0 and d>0 its a local minima

Answer 2

3x^2 - 3e^5y^2