Question

Find the average rate of change for the given function from x = −1 to x = 2. Graph of f of x equals negative three x plus 2

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)=-3x+2\quad \begin{cases} x_1=-1\\ x_2=2 \end{cases}\implies \cfrac{f(2)-f(-1)}{2-(-1)}\implies \cfrac{f(2)-f(-1)}{2+1} \\\\\\ \cfrac{[-3(2)+2] - [-3(-1)+2]}{3}\implies \cfrac{[-6+2]-[3+2]}{3} \\\\\\ \cfrac{-4-5}{3}\implies \cfrac{-9}{3}\implies -3`