Question 922835
 




if {{{f(x)=x^3}}} then

1. replace {{{x}}} with {{{a}}}

{{{f(a)=a^3}}}


2. replace {{{x}}} with {{{a+h}}}

{{{f(a+h)=(a+h)^3}}}

{{{f(a+h)=(a+h)(a+h)(a+h)}}} ...multiply all

{{{f(a+h)=a^3+3a^2*h+3ah^2+h^3}}}



3. replace {{{x}}} with {{{x+h}}}

 {{{f(x+h)-f(x)/h}}}, {{{h}}} does not equal {{{0}}}

{{{f(x+h)-f(x)/h=((x+h)^3-x^3)/h}}}

{{{f(x+h)-f(x)/h=(h^3+3h^2x+3hx^2+cross(x^3)-cross(x^3))/h}}}

{{{f(x+h)-f(x)/h=(h^3+3xh^2+3hx^2)/h}}}

{{{f(x+h)-f(x)/h=h(h^2+3xh+3x^2)/h}}}

{{{f(x+h)-f(x)/h=cross(h)(h^2+3xh+3x^2)/cross(h)}}}

{{{f(x+h)-f(x)/h=h^2+3xh+3x^2}}}