Question

What is the maximum value of the function f(x, y) = x^2(1 + 3y) + x^3 + y^3 + y^2(1 + 3x) + 2xy over the region x=0; y=0; x + y=1.

(a) 0

(b) -1

(c) Has no maximum value

(d) 2

This question was posed to me during an internship interview.

My question comes from Maxima and Minima of Two Variables in portion Maxima and Minima of Engineering Mathematics

Answer 1

Correct answer is (d) 2

Easy explanation: Rewrite the function as

f(x, y) = (x + y)^2 + (x + y)^3

Put x + y = 1

= 2.