On the first day of the year, diego had $700 in his savings account and started spending $35 a week. his brother juan had $450 and started saving $15 a week. after how many weeks will the brothers have the same amount? what will that amount be?
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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.