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In: Math

Find the local maximum and minimum values and saddle point(s) of the function. If you have...

Find the local maximum and minimum values and saddle point(s) of the function. If you have three dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter NONE in any unused answer blanks.) f(x, y) = x^3 – 27xy + 27y^3

Solutions

Expert Solution

Solution:-

Differentiantin with respect to 'x'

Differentiantin with respect to 'y'

Now

----------------------------------(2)

solving (1) & (2),

The point are

<0

The local maxima at this point (0,0)

(3,1)

Local minima at (3,1)

The saddle point is at

The point is shown in the figure


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