(4) Find all the maxima and minima of the following functions. (a) f : IR2 - R, f (x, y) = x3 + xy+ y's. xy (b ) f : IR 2 - IR , f ( x , y ) = x2 + 1 2 + 1 (c) f : IR3 -+ IR, f (x, y, z) = x4+ 14+ 24. n n (d) f : In - R, f(x1, . .., Xn) = _ _ajaxix;, where (a1, . .., an) is a given nonzero vector in R". i=1 =1