In: Math
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
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