Question

Find the average rate of change of the function on the interval, specified for real number b ???

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)= 6x^2-7 \qquad \begin{cases} x_1=1\\ x_2=b \end{cases}\implies \cfrac{f(b)-f(1)}{b - 1}`

`\cfrac{[6(b)^2-7]~~ - ~~[6(1)^2-7]}{b-1}\implies \cfrac{6b^2-6}{b-1}\implies \cfrac{6(b^2-1)}{b-1}\implies \cfrac{6(b^2-1^2)}{b-1} \\\\\\ \cfrac{6(b-1)(b+1)}{b-1}\implies 6(b+1)`