tersecting of the cone z
2 = x
2 + y
2 and the plane x + y − z + 2 = 0
42. (a) Find the maximum of the function f : R
n → R defined by
f(x1, x2, . . . , xn) = Yn
k=1
x
2
k
subject to the constraint Xn
k=1
x
2
k = 1.
(b) Deduce that for x = (x1, x2, . . . , xn) ∈ R
n
:





Yn
k=1
xk





≤

kxk
√
n
n