Question 398090
{{{f(x)=3x^3-x^2+8x-1}}}
{{{f(a+h)=3(a+h)^3-(a+h)^2+8(a+h)-1=3(a^3+3a^2h+3ah^2+h^3)-(a^2+2ah+h^2)+8a+8h-1=3a^3+9a^2h+9ah^2+3h^3-a^2-2ah-h^2+8a+8h-1}}}
{{{(f(a+h)-f(a))/h=(3a^3+9a^2h+9ah^2+3h^3-a^2-2ah-h^2+8a+8h-1-(3a^3-a^2+8a-1))/h
=(3a^3+9a^2h+9ah^2+3h^3-a^2-2ah-h^2+8a+8h-1-3a^3+a^2-8a+1)/h=(9a^2h+9ah^2+3h^3-2ah-h^2+8h)/h=9a^2+9ah+3h^2-2a-h+8}}}