Let f(x)=x^3 - 14x.
Calculate the difference quotient (f(3+h) - f(3))/h for h=0.1
[ f(3 + h) - f(3) ] / h =
[ (3 + h)^3 - 14 (3 + h) - [ (3)^3 - 14(3)] ] / h =
[ 27 + 3*3^2*h + 3*3*h^2 + h^3 - 42 - 14h - 27 + 42] / h =
[ 27h + 9 h^2 + h^3 - 14h ] / h =
[13 + 9h + h^2] =
[ 13 + 9(0.1) + (0.1)^2] = 13.91
