The function g is piecewise linear on 0≤x≤8 with the following properties:
• On 0≤x≤3, the slope of g is 2.
• On 3<x≤5, the slope of g is −1.
• On 5<x≤8, the slope of g is 4.
Let f(x)=g′(x). At which of the following x–values does f attain its minimum on the interval 0<x<8?
a) x=3
b) x=4
c) x=5
d) x=2