Hey I was wondering if anyone can tell me if i am doing this right.(adsbygoogle = window.adsbygoogle || []).push({});

f(x,y) = xy^2 ; R is the circular disk x^2+y^2<=3

So first i took the gradient, since I know a mix/min can exist if the gradient is equal to 0.

Gradient of X= y^s

Gradient of Y= 2xy

So the point (0,0) can be considered right?

Anyway, I know I have to test region edges, so I parameterized the equation.

r(t) = <radical 3 cos(t),radical 3 sin(t)>

i plugged those values of x and y into my equation , and then took the derivative.

After some simplification, I came up with

sin(t)(3*radical3*cos(t)^2-3*radical3)

t= 0, pi, pi/2, 3pi/2 (right?)

so i found the x and y value when t is equal to those values

in conclusion, i have these points.

(0,0)

(0,radical3)

(0,-radical3)

(radical3,0)

(-radical3,0)

I tested these values in the equation xy^2 = f(x,y)

and found that there is no max or min....i dont think this is right.

Can someone help me find my mistake?

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# Homework Help: MAX/MINS with multivariables

Can you offer guidance or do you also need help?

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