At time tequals 0, water begins to drip out of a pipe into an empty bucket. After 64
minutes, there are 8
inches of water in the bucket. Write a linear function rule to model how many inches of water w are in the bucket after any number of minutes t.
The linear function rule is W = ___

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.