The length and width of the rectangle in c are three times the the length and width of the rectangle in b. the perimeter and area of the rectangle in c are how many times those measures in b.
b: width: 4 cm c: width: 12 cm
length: 3 cm length: 9 cm

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.