Question

Find the average rate of change for f(x)=x^3+x from 1 to 2 and the equation of the secant line containing (1, f(1)) and (2, f(2)). Please show all of your work.

Answer 1

\[f(2)=2^3+2=10\]
\[f(1)=1^3+1=2\]
\[\frac{f(2)-f(1)}{2-1}=\frac{10-2}{1}=8\]

Answer 2

that is the slope, now use
\[y-y_1=m(x-x_1)\] with
\[x_1=1,y_1=2,m=8\] to get your answer