Use the digits 3,5, and 7 to make two three-digit numbers with the greatest possible sum

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.

to find the perimeter, you add up all the lengths of the sides. in this case you would have to add up 18+22+40+80 which equals 160.

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