Question

Let f(x)=x^2-4. What is the average rate of change of f(x) from -5 to -2

Answer 1

`\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\\\\ f(x)= x^2 - 4 \qquad \begin{cases} x_1=-5\\ x_2=-2 \end{cases}\implies \cfrac{f(-2)-f(-5)}{-2 - -5} \\\\\\ \cfrac{[(-2)^2 -4]~~ - ~~[(-5)^2 -4]}{-7}\implies \cfrac{[0]~~ - ~~[21]}{-7}\implies \text{\LARGE 3}`