Determine the maximum and minimum of each function on the given interval.

Question

a) ���� = 2x^3�� − 9x^2�� ,−2 ≤ x� ≤ 4
b) ���� = 12x� − x^3�� , � x∈ �[−3,5]

Answer 1

I will do the first one, you do the second in the same way

a) y = 2x^3 - 9x^2 , -2 ≤ x ≤ 4

dy/dx = 6x^2 - 18x
= 0 for a max/min
6x(x-3) = 0
x = 0 or x = 3, both are within our given domain

if x = 0 , y = 0
if x = 3 , y = 56 - 81 = -27

so the max is 0 and the min is -27

Answer 2

should have checked the end points
if x = -2 , y = -16 - 36 = -52
if x = 4 , y = -16

revised answer:

the max is 0 and the min is -52 within the given domain.