Sonya made a scale drawing of her county. She used the scale
0.5 cm = 10 km. The distance between
the northernmost point and the
southernmost point in the drawing is
11 cm. What is the actual distance
between the two points?

answer: 1) twenty-seven times y

              2) twenty-seven multiplied by y

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.