Question

Let m(k)=5k6+6k2 . What is the average rate of change of m(k) with respect to k as the value of k changes from 2 to -9

Answer 1

`\bf slope = \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{f(x_2)-f(x_1)}{x_2-x_1}\leftarrow \begin{array}{llll} \textit{average rate}\\ \textit{of change} \end{array}\\\\ -----------------------------\\\\ m(k)=5k^6+6k^2\qquad \begin{cases} x_1=2\\ x_2=-9 \end{cases}\implies \cfrac{m(-9)-m(2)}{-9-2}`