Please help with calculus question!

Calculus
Tutor: None Selected Time limit: 1 Day

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!

Theorem
Let f be a function with two variables with continuous second order partial derivatives fxx, fyy and fxy at a critical point (a,b). Let

D = fxx(a,b) fyy(a,b) - fxy2(a,b)
  1. If D > 0 and fxx(a,b) > 0, then f has a relative minimum at (a,b).
  2. If D > 0 and fxx(a,b) < 0, then f has a relative maximum at (a,b).
  3. If D < 0, then f has a saddle point at (a,b).
  4. If D = 0, then no conclusion can be drawn.

We now present several examples with detailed solutions on how to locate relative minima, maxima and saddle points of functions of two variables. When too many critical points are found, the use of a table is very convenient.

=-2x+10

=3y^2-6y-9

x=5

y=9 or 2

minima= (5, 2)

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

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Jul 22nd, 2015
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Jul 22nd, 2015
Dec 5th, 2016
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