Brandon graphed y = 80 - 5x to represent the number of gallons of water left in a pool that has been draining for x minutes.
100
190
80
70
eo
50
Water (gal)
40
30
20
10
410 24 8
8 10 12 14 18 20
Time (min)
What is a reasonable domain for this situation?

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.

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step-by-step explanation:

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