Question

H(x)=x^2-1 what is the average rate of change of h over the interval −3≤x≤−1

Answer 1

$slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array}\\\\[-0.35em] \rule{34em}{0.25pt}\\\\ h(x)=x^2-1 \qquad \stackrel{-3\leqslant ~~x~~\leqslant -1}{\begin{cases} x_1=-1\\ x_2=-3 \end{cases}}\implies \cfrac{h(-3)-h(-1)}{-3-(-1)} \\\\\\ \cfrac{[(-3)^2-1]~~ -~~[(-1)^2-1]}{-3+1}\implies \cfrac{8~~-~~0}{-2}\implies -4$