Joe and Will both work as cooks at Burger Palace. Each prepares hamburgers at a different speed, as shown by the functions below:

J(b) = 14b + 7
W(b) = 7b + 42

where b represents the number of hamburgers cooked and J(b) and W(b) represent the amount of time each cook takes in minutes. At what value of b will their cooking time be equivalent?

a

step-by-step explanation:

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.