8 2/3 is the answer
step-by-step explanation: just use a calculator
Check where the first-order partial derivatives vanish to find any critical points within the given region:
The Hessian for this function is
with , so unfortunately the second partial derivative test fails. However, if we take we see that for different values of ; if we take we see takes on both positive and negative values. This indicates (0, 0) is neither the site of an extremum nor a saddle point.
Now check for points along the boundary. We can parameterize the boundary by
with . This turns into a univariate function :
At these critical points, we get
We only care about 3 of these results.
So to recap, we found that attainsa maximum value of 4096 at the points (0, 8) and (0, -8), anda minimum value of -1024 at the point (-8, 0).