If Lupe walk 0 miles, he will earn $50 for his library fundraiser just by signing up to help. But if Lupe walks 1 mile, he will earn $60 for his library fundraiser by signing up & walking, $10 for walking the one mile & $50 just for signing up to help. How much did Lupe make per 1 mile?

$10

Step-by-step explanation:

Given that:

Amount earned for 0 mile = $50 (earned for signing up)

Amount earned for walking 1 mile = $60 ($50 for signing up and $10 for. Walking)

Hence, the amount earned per mile walked according to the information given is $10

Total amount earned =. Sign up fee +. Walking fee

$60 = $50 + walking fee

Walking fee = $60 - $50

Walking fee =. $10

Miles walked = 1 mile

Hence , amount earned per mile = $10

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.