Aruler with dimensions 2cm by 5cm is placed underneath a right-right-angled triangle. the area is clearly less than that of both individual shapes. the percentage of area now showing, compared with the sum of the areas of each shape

-22

times both sides by 2, times () by 8, add alile terms, move terms, add alike and caculate divide both sides by 3

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.