Lucille Davidson

2021-12-08

Find the absolute maximum and minimum values of $f(x,y)={x}^{2}+{y}^{2}-2x+1$ on the unit disc ${x}^{2}+{y}^{2}\le 1$ .

Marcus Herman

Beginner2021-12-09Added 41 answers

Step 1

Given function is:

Step 2

Let,

Then,

Step 3

Let,

Then,

Taking partial derivatives,

Now,

r=0, t=0

Step 4

If r=0 only, then

If t=0 only, then x=rt,

From this, at end point

Step 5

Hence, the absolute maximum values is 2 and absolute minimum value is 1.

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