Question

Find the average rate of change for the given function on the given interval

3. f(x)=x2-4x; -2 ≤x≤ 4
4. f(x)=2x-1; [0, 3]

Answer 1

3)


`\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}\\\\ -------------------------------\\\\ %x2-4x; -2 ≤x≤ 4 f(x)=x^2-4x \qquad \begin{cases} x_1=-2\\ x_2=4 \end{cases}\implies \cfrac{f(4)-f(-2)}{4-(-2)} \\\\\\ \cfrac{[4^2-4(4)]~~-~~[(-2)^2-4(-2)]}{4+2}\implies \cfrac{[16-16]~~-~~[4+8]}{6} \\\\\\ \cfrac{0-12}{6}\implies \cfrac{-12}{6}\implies \cfrac{-2}{1}\implies -2`