Jennifer is saving money to buy a bike. The bike costs $336. She has $128 saved, and each week she adds $16 to her savings. How long will it take her to save enough money to buy the bike? It will take her \weeks to save for the bike.

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.