Question
Asked Mar 2, 2020
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Find the absolute maximum and minimum values of f on the set D.
f(x, y) = 4x + 6y – x² – y2 + 9,
D = {(x, y) | 0 s xs 4, 0 s ys 5}
absolute maximum value
absolute minimum value
%3!
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Find the absolute maximum and minimum values of f on the set D. f(x, y) = 4x + 6y – x² – y2 + 9, D = {(x, y) | 0 s xs 4, 0 s ys 5} absolute maximum value absolute minimum value %3!

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Expert Answer

Step 1

Given function and its set of domain is as below.

Calculus homework question answer, step 1, image 1

Step 2

Complete the square on the right side of the function as shown below.

Calculus homework question answer, step 2, image 1

From the above function it is clear that the term in the square brackets will always greater than or equal to 0.

Step 3

For maximum value:

The function has maximum value if the terms in the braces have least value. The least value of (x – 2)2 and (y – 3)2 is when x = 2 and y = 3.

Calculus homework question answer, step 3, image 1

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