Question 7 Automated tractors can mow lawns without being driven by a person. A company runs trials using fields of different sizes and records the amount of time it takes the tractor to mow each field. Find the line of
best fit for the data below.
Time
Acres
(hours)
5
15
7
10
10
22
17
323
18
46.8
20
34
22
39.6
25
75
C2021 Illuminate Education Inc
7:28
hp

∞ this is your sign

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.