Calculus question

Question

Find the average value over the interval 2≤x≤9 of the function f, the graph of which is shown above. Round your answer to the nearest tenth.

Answer 1

about 4.3

first section has average (7+4)/2 = 5.5

2nd section: (7+1)/2 = 4

3rd: ( 5+1)/2 = 3

last: 5

average them with equal weights for the last three sections and 1/2 weight for the 1st section

or double weights for the last three and single weight for the 1st section

[2(5.5+4+3)+5]/7

=30/7 = about 4.29= average over 2<x<9

f(x) = { 3x if 2<x<3

-3x+ 16 if 3<x<5

2x-9 if 5<x<7

5 if 7<x<9}

(5,1),(7,5) have a line through them with slope = 4/2=2 = (y-1)/(x-5)

y=2x-9

(3,7),(5,1) have line's slope = (7-1)/(3-5) = -6/2 =-3 = (y-1)/(x-5)

y=-3x+16