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Mathematics-Online problems:

Interactive Problem 182: Critical Points of a Function of two Variables

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Given the function

$\displaystyle f(x,y)=x^4+y^4+2x^2y^2-26x^2-10y^2\,. $

Find the first and second partial derivatives of $ f$.

         $ f_x\ =\ $ $ x^3$ + $ xy^2$ + $ x$

         $ f_y\ =\ $ $ y^3$ + $ x^2y$ + $ y$

         $ f_{xx}\ =\ $ $ x^2$ + $ y^2$ +

         $ f_{xy}\ =\ $ $ xy$

         $ f_{yx}\ =\ $ $ xy$

         $ f_{yy}\ =\ $ $ x^2$ + $ y^2$ +

Insert in the following table the critical points and mark their typ. Start with the point whose distance to the origin is minimal.

point n.a. local minimum local maximum saddle point
$ \Big(\pm\big($ $ \big)^\frac{1}{2}$ , $ \pm\big($ $ \big)^\frac{1}{2}\Big)$
$ \Big(\pm\big($ $ \big)^\frac{1}{2}$ , $ \pm\big($ $ \big)^\frac{1}{2}\Big)$
$ \Big(\pm\big($ $ \big)^\frac{1}{2}$ , $ \pm\big($ $ \big)^\frac{1}{2}\Big)$

   
(Source unknown)

see also:

  automatically generated: 8/11/2017