Which is the more reasonable measurement of the diameter of a human hair: 1.8 ⋅ 10^−2 mm or 1.8 ⋅ 10^2 mm? justify your answer.

Its a very small measurement.

1.8 * 10^2 =   180 mm = 18 cms

1.8 * 10^-2  = 0.018 mm  <    Thats the one

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.