Determine the location of any maxima, minima, or saddle points for: (tell what each one is) f(x,y)=y^3-3y^2-x^2-9y+10x-60

Thank you for the opportunity to help you with your question!

df/dx = -2x+10 = 0

x = 5

df/dy = 3y^2-6y-9 =0

y = -1 or y =3

(5,-1)

(5,3)

fxx = -2

fyy = 6y-6

fxy = 0

delta = fxx*fyy = 12-12y

for (5,-1) delta = 24 >0 (5,-1) is local minimum

for (5,3) delta = 12-36 = -24 <0 (5,3) is local maximum

sorry (5,-1) is local maximum,

(5,3) is saddle point

Then what's the minimum?

no local minimum

ok. Perfect. Thanks!

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