Question

Calculate the average rate of change forf(x) = 8x + 2from x to x + h.

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}\\\\ f(x)=8x+2 \qquad \begin{cases} x_1=x\\ x_2=x+h \end{cases}\implies \cfrac{f(x+h)-f(x)}{(x+h)-x} \\\\\\ \cfrac{[8(x+h)+2]~~ -~~[8x+2]}{h}\implies \cfrac{[8x+8h+2]-8x-2}{h} \implies \cfrac{8h}{h}\implies 8`