Haraya owns two triangular plots of land, ABC and ACD. The length of AD is 59 m, BC is 50 m, and AC is 70 m. The size of ADCis 72º and ACBis 22º. The following diagram shows this information.

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.