A rectangular yard is fenced in using 290 feet of custom fence. Your friends really like the fence and decide to fence in their yard using the same fence. Their yard is similar but has a scale factor of 2 times the size of
yours, how much fence, to the nearest foot, will they have to purchase

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.

you need to give us more information since we can't answer