Michael is making cookies. Each batch uses 3 cups of flour. He plans to use less than 41 cups of flour for cookies so that he has enough left to make muffins. He has already used 5 cups of flour for cookies. How many more batches of cookies can Michael make?

Fewer than 12

Greater than 15.3333…

Fewer than 15.3333…

Greater than 12

if x = 1, then the answer is 3.5

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.