Question

Identify any extrema of the function by recognizing its given form or its form after completing the square. verify your results by using the partial derivatives to locate any critical points and test for relative extrema.

Answer 1

Step 1:

The function is .

Apply partial derivative on each side with respect to .

The function is .

Apply partial derivative on each side with respect to .

Step 2:

Find critical points, solve and .

The critical point .

Completing the squares.

The function has a relative minimum at if .

.

The function has relative minimum at  .

Solution:

The function has relative minimum at  .