Question

Given f'(x)=(x-4)(4-2x), find the x-coordinate for the relative maximum on the graph of f(x)

Answer 1

critical values x= 4, 2

Answer 2

on what interval and do you know what f(x) is?

Answer 3

you can draw a number line and test the following intervals by choosing a number representative:
(-inf,2)
(2,4)
(4,inf)
see if f'<0 or f>0 on these intervals by choosing a number from each interval in pluggin' into f'(x)

Answer 4

f'>0 means f is increasing
f'<0 means f is decreasing

Answer 5

ok I got 4

Answer 6

(I haven't done the problem; so let's check it together )
so you did a number line...