Please help with calculus question!

label Calculus
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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

Jul 22nd, 2015

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  

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jul 22nd, 2015

sorry (5,-1) is local maximum, 

(5,3) is saddle point 

Jul 22nd, 2015

Then what's the minimum?

Jul 22nd, 2015

no local minimum 

Jul 22nd, 2015

ok. Perfect. Thanks!

Jul 22nd, 2015

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