What is the average rate of change of y with respect to x over the interval [–3, 4] for the function y = 2x + 2?

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aastra1 aastra1

02-11-2017
Mathematics

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What is the average rate of change of y with respect to x over the interval [–3, 4] for the function y = 2x + 2?

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jdoe0001 jdoe0001 · Answer 1 · 2017-11-02T21:53:15+01:00

[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}\\\\ -------------------------------\\\\ \stackrel{f(x)}{y}=2x+2 \qquad \begin{cases} x_1=-3\\ x_2=4 \end{cases}\implies \cfrac{f(4)-f(-3)}{4-(-3)}\implies \cfrac{f(4)-f(-3)}{4+3} \\\\\\ \cfrac{[2(4)+2]~~-~~[2(-3)+2]}{7}\implies \cfrac{10-(-4)}{7}\implies \cfrac{10+4}{7}\implies \cfrac{2}{1}[/tex]