Question

(a) Differentiate the following function
y = x^2 e^x
(b) A cosmetic company is planning the introduction of a promotion of a new lipstick line. The marketing research department after test marketing the new line in a carefully selected city found that the demand in the city is approximately given by p = 12e^(-x), where x which should be within this range, 0 ≤ x ≤ 2 were thousand lipsticks sold per week at a price of Kenya shillings. At what price will the weekly revenue be at maximum? What is the maximum weekly revenue