Question

Given the function h(x) =-x^2+3x+8, determine the average rate of change of

the function over the interval 1 < x < 6?

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+3x+8 \qquad \begin{cases} x_1=1\\ x_2=6 \end{cases}\implies \cfrac{h(6)-h(1)}{6-1} \\\\\\ \cfrac{[-(6)^2+3(6)+8]~~ -~~[-(1)^2+3(1)+8]}{5}\implies \cfrac{-10~~ - ~~(10)}{5} \\\\\\ \cfrac{-20}{5}\implies -4`