calc_tutorial_14_7_032

Problem Statement

{2,3,4,5,6,7,8,9}

Determine the global extreme values of the function on the given set without using calculus.

Step 1

Question Sequence

Question 1

Recall the existence of global extrema. Let f(x, y) be a continuous function on a closed, bounded domain . Then f(x, y) has both a minimum and a maximum value on .

The given domain is D = {(x, y) | x² + y² ≤ 5}.

This domain is . Also, f(x, y), being an exponential function, continuous.

Thus f(x, y) attain both a maximum and minimum on D.

Correct.

Incorrect.

Step 2

Question Sequence

Question 2

Write

Observe that f(x, y) will attain its maximum value when attains its value. This will occur when x² + y² attains its value. Since x² ≥ 0 and y² ≥ 0, this value of x² + y² is x² + y² = .

Find the maximum value of f(x, y).

Correct.

Incorrect.

Step 2

Question Sequence

Question 3

Write

Observe that f(x, y) will attain its minimum value when attains its value. This will occur when x² + y² attains its value. Since x² ≥ 0 and y² ≥ 0, this value of x² + y² is x² + y² = .

Find the minimum value of f(x, y).

Correct.

Incorrect.