find the minimum and maximum value of f(x) = |x - 4| + 4 on the interval [-3, 5]

Question

Please show all your work and steps on how you got the answer.

Answer 1

x=4 makes f(x) a minimum, both absolute and relative, local minimum

the absolute value of x-4 has a minimum when x-4 = 0 or x=4

0 + 4 = 4 = minimum value of f(x)

absolute value of -3-4 = 7

7+4 = 11 = the maximum f(x) on the interval [-3,5]

f(-3) = the maximum in the interval

just to be sure plug in the other endpoint of the interval x=5

5-4 = 1. 1+4 = 5 < 11 so f(5) is not a minimum or maximum