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Mathematics, 17.09.2019 06:30 jeffrey74081

At the 2009 x games, one skateboarder completed 34 ollies in 30 seconds. if he could keep up the rate, what would be his rate per minute?

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Answers: 1
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Answer from: Quest
Answer

1 number

explanation

if we use a graphing calculator, there is only one such number c\in[0.5,0.75] that satisfies the conclusion of the mean value theorem, that is, a number c\in[0.5,0.75] such that

  f'(c) = \dfrac{f(0.75) - f(0.5)}{0.75-0.5},

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.

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