Question

What is the average rate of change of the function f(x) on the interval etc… PLEASE HELP

Answer 1

Check the picture below.

`\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\\begin{cases} x_1=2\\ x_2=4 \end{cases}\implies \cfrac{f(4)-f(2)}{4 - 2}\implies \cfrac{1~~ - ~~1}{2}\implies \cfrac{0}{2}\implies \text{\LARGE 0}`