Question

20 POINTS

What is the rate of change of the equation f(x) = ¯x² + 6x + 5 for the interval 0≤x≤ 3?

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+6x+5 \qquad \begin{cases} x_1=0\\ x_2=3 \end{cases}\implies \cfrac{f(3)-f(0)}{3 - 0} \\\\\\ \cfrac{[(3)^2+6(3)+5]~~ - ~~[(0)^2+6(0)+5]}{3}\implies \cfrac{27}{3}\implies \text{\LARGE 9}`