Question

Need help please

What is the average rate of change of the function over the interval x = 0 to x = 8? f (x)=2x+3/3x−3

Answer 1

`\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+3}{3x-3} \qquad \begin{cases} x_1=0\\ x_2=8 \end{cases}\implies \cfrac{f(8)-f(0)}{8-0}`


`\bf \cfrac{\left[ (2(8)+3)/(3(8)-3) \right]~~-~~\left[ (2(0)+3)/(3(0)-3) \right]}{8}\implies \cfrac{\left[ (19)/(21) \right]~~-~~\left[ (3)/(-3) \right]}{8} \\\\\\ \cfrac{(19)/(21)-(-1)}{8}\implies \cfrac{(19)/(21)+1}{8}\implies \cfrac{(40)/(21)}{\quad 8\quad }\implies \cfrac{(40)/(21)}{\quad (8)/(1)\quad }\implies \cfrac{40}{21}\cdot \cfrac{1}{8} \\\\\\ \cfrac{5}{21}\cdot \cfrac{1}{1}\implies \cfrac{5}{21}`