Question

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) = x3 – 27xy + 27y3 maximum I ) = ) = (smaller x value) (larger x value) fc fc minimum fo ) = (smaller x value) (larger x value) ). 1 fe saddle points 1 ( ( ) (smallest x value) ) (largest x value)

Answer 1

f(n.) = 7,29*2y + 27y3 fx = 3x² - azy fy - 2ax +814² point fro, fy=0 32.249 so, - 27 x t fly"=0 - 19: o -* +3y=0 .: SO, yo x=3, y=1 :(0,0) and (3, 1) are critical points fans 6x fazy 1624, fay = -27 faxi fyy -(fxy) at (oo) Do (O) (O) - (-2). -729 <o since D20 (oo) i Saddle point at (3,1) (18) (162) - (-20)2 = 2187 sine o >o, faux > 0 '. (3,1) is minimum minimum f(3,1) - -27 saddle point flo 0) =