Question

Find the average rate of change over the given interval: f(x) = 3^x, [1, 4]

Answer 1

$\bf slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array}\\\\ -------------------------------\\\\ f(x)= 3^x \qquad \stackrel{[1,4]}{\begin{cases} x_1=1\\ x_2=4 \end{cases}}\implies \cfrac{f(4)-f(1)}{4-1}\implies \cfrac{3^4~-~3^1}{3} \\\\\\ \cfrac{81-3}{3}\implies \cfrac{78}{3}\implies 26$