Question

SOLVED THE MIN JSUT NEED HELP FIGURING OUT TO DO THE MAX.
Determine the maximum value and the minimum value of f (x, y) = x2 + y2 − x − y on the closed unit disk D : x2+y2 ≤ 1. (Hint: Recall that the unit circle x2+y2 = 1 can be parametrized as x = cos t, y = sin t.)

Answer 1

when i take the derivative
f'(t) = -cos(t) + sin(t) = 0
then
sin(t) = cos(t)
t = pi/4
is that look right?

Answer 2

YES

Answer 3

then
min = 1-2/sqrt(2) = -.414
and max would have to be 1 i guess

Answer 4

when t = -pi/4, sin = -cos
max = 1 -(cos-cos) = 1

Answer 5

wow i was off
t = 5pi/4 is also a solution to sin = cos
max = 1+2/sqrt(2) = 2.414