For the function, find the average rate of change of f from 1 to x:f(x)-f(1)/x-1

Question

x does not equal 1

f(x) = x3 + x

Answer 1

avg rate is slope of secant:

[f(x)-f(1)]/[x-1]
= [(x^3+x)-(1^3+1)]/[x-1]
= (x^3+x-2)/(x-1)
= x^2+x+2