If f(x)=x^3−x, what is the average rate of change of f(x) over the interval [1, 5]? a)29.5 b)30 c)43 d)120

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03-01-2018
Mathematics

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If f(x)=x^3−x, what is the average rate of change of f(x) over the interval [1, 5]? a)29.5 b)30 c)43 d)120

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jdoe0001 jdoe0001 · Answer 1 · 2018-01-03T23:31:12+01:00

jdoe0001 jdoe0001

03-01-2018

[tex]\bf slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array}\\\\ -------------------------------\\\\ f(x)= x^3-x \qquad \begin{cases} x_1=1\\ x_2=5 \end{cases}\implies \cfrac{f(5)-f(1)}{5-1} \\\\\\ \cfrac{[5^3-5]~-~[1^3-1]}{4}\implies \cfrac{125-5~~-~~0}{4}\implies \cfrac{120}{4}\implies 30[/tex]

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