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Kork

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Find the maximum and minimum values of f(x,y) = x+2y on the disk

x

I have this for now:

f_1(x,y) = 1

f_2(x,y) = 2

x=cos(t) and y=sin(t)

I have that g(t) = x(t) + 2*y(t) --> g(t) = cost(t) + 2*sin(t)

g'(t) = 0 = 2*cost-sin(t)

Then I can see that:

2cos(t)/cos(t) -sin(t)/cos(t) = 0/cos(t) --> tan = 2

That is the parameterization, right?

From this point I have no idea what to do.

x

^{2}+y^2 ≤1I have this for now:

f_1(x,y) = 1

f_2(x,y) = 2

x=cos(t) and y=sin(t)

I have that g(t) = x(t) + 2*y(t) --> g(t) = cost(t) + 2*sin(t)

g'(t) = 0 = 2*cost-sin(t)

Then I can see that:

2cos(t)/cos(t) -sin(t)/cos(t) = 0/cos(t) --> tan = 2

That is the parameterization, right?

From this point I have no idea what to do.

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