The distance from your house to the ice cream shop is 12 miles. your best friend’s house is on the segment between your house and the ice cream shop, and his house is 3 miles from the ice cream shop. how many miles is your house from your best friend’s house?

answer:     true

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.