Question

Calculate the average rate of change for the function f(x)=x^4+3x^3-5x^2+2x-2, from x=-1 to x=1

Answer 1

$\bf slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ f(x_2)}}-{{ f(x_1)}}}{{{ x_2}}-{{ x_1}}}\impliedby \begin{array}{llll} average\ rate\\ of\ change \end{array}\\\\ -------------------------------\\\\ f(x)= x^4+3x^3-5x^2+2x-2 \qquad \begin{cases} x_1=-1\\ x_2=1 \end{cases}\implies \cfrac{f(1)-f(-1)}{1-(-1)} \\\\\\ \cfrac{[1+3-5+2-2]~~-~~[1-3-5-2-2]}{1+1}\implies \cfrac{[-1]~~-~~[-11]}{2} \\\\\\ \cfrac{-1+11}{2}\implies \cfrac{10}{2}\implies 5$