MATH SOLVE

3 months ago

Q:
# Need help pleaseWhat is the average rate of change of the function over the interval x = 0 to x = 8? f (x)=2x+3/3xβ3

Accepted Solution

A:

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

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

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