Question

Find the max and min values of f (x, y) = cos t^2 + sin t^2 − cos t− sin t

Answer 1

F(x,y)=1-cost-sint but i do not know where to go from here

Answer 2

f(x,y) = an equation with no xs or ys ???

Answer 3

cos^2 + sin^2 = 1 regardless

Answer 4

i read that wrong tho lol

Answer 5

the original equation is : f (x, y) = x2 + y2 − x − y on the closed unit disk D : x^2+y^2 ≤ 1. (Hint: Recall that the unit circle x^2+y^2 = 1 can be parametrized as x = cos t, y = sin t.) so i just substituted x and y values

Answer 6

i have to find the max and min values

Answer 7

you need to find your partials right?

Answer 8

yes and i have done that i have found the local min value (1/2,1/2)

Answer 9

i just dont know how to find the max

Answer 10

the links aint up and running so youll have to copy paste this to see

http://www.wolframalpha.com/input/?i=+f+%28x%2C+y%29+%3D+x2+%2B+y2+%E2%88%92+x+%E2%88%92+y

Answer 11

it has no max; just like a parabola on an x,y plane has no max

Answer 12

f(x, y) = x2 + y2 −x−y

df/dx = 2x −1

df/dy = 2y -1

when 2x-1=0 and 2y-1=0, you have "normal" vector that point up to indicate a min or max of the surface

Answer 13

or at least a critical point, it could also be a saddle back but not this time