pgirl24501
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PLZ HELP ME!! You will earn 15 POINTS and BRAINLIEST!!!!
What is the average rate of change of the function over the interval x = 0 to x = 6? f(x)=2x−1
                                                   ____
                                                   3x+5

Respuesta :

[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)=\cfrac{2x-1}{3x+5} \qquad \begin{cases} x_1=0\\ x_2=6 \end{cases}\implies \cfrac{f(6)-f(0)}{6-0}[/tex]

[tex]\bf \cfrac{\left[ \frac{2(6)-1}{3(6)+5} \right]~~-~~\left[ \frac{2(0)-1}{3(0)+5} \right]}{6}\implies \cfrac{\left[ \frac{11}{23}\right]~~-~~\left[-\frac{1}{5} \right]}{6} \\\\\\ \cfrac{\frac{11}{23}+\frac{1}{5}}{6}\implies \cfrac{\quad \frac{78}{115}\quad }{\frac{6}{1}}\implies \cfrac{78}{115}\cdot \cfrac{1}{6}\implies \cfrac{13}{115}[/tex]