A recipe calls for 21 oz of flour for every 5 oz of milk. If you use 25 oz of milk, how much flour should you use?

105 oz of flour

Divide 21 by 5 (4.2)

Multiply 25 by 4.2 (105)

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.