, 24.01.2020legendman27

# Find the absolute maximum and absolute minimum of the function f(x, y)=2x3+y4f(x, y)=2x3+y4 on the region {(x, y)|x2+y2≤64}{(x, y)|x2+y2≤64} ignore unneeded answer blanks, and list points lexicographically.

## Answers

The answer maybbe c

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 attains

a maximum value of 4096 at the points (0, 8) and (0, -8), anda minimum value of -1024 at the point (-8, 0).

Do you know the answer?

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