Question

dentify 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. (If an answer does not exist, enter DNE.) g(x, y) = (x − 8)2 + (y − 1)2

Answer 1

There will be a local minimum at (8 , 1)

Explanation:

Let the function be given as:

G(x , y) = (x − 8)2 + (y − 1)2

This is a completed square, which means that the equation is identical to that of a circle. Hence from the equation again, the points will be as follows:

x ordinates = x - (+8)

y ordinates = y- (+1)

Hence the points will be:

(x , y) = (8 , 1)