Question 287329
{{{ f(x)=2x^2-x }}}
{{{ f(x+h)=2(x+h)^2-(x+h) }}}
(Note the parentheses!. Without them it's nearly impossible to do this correctly.)
{{{ f(x+h)=2(x^2+2xh + h^2)-(x-h) }}}
{{{ f(x+h)=2x^2+4xh + 2h^2-(x+h) }}}
{{{ f(x+h)=2x^2+4xh + 2h^2-x-h }}}<br>
Now that we have f(x+h) we can write {{{(f(x+h) - f(x))/h}}}:
{{{(f(x+h) - f(x))/h = ((2x^2+4xh + 2h^2-x-h) - (2x^2-x))/h = (2x^2+4xh + 2h^2-x-h - 2x^2+x)/h = (4xh + 2h^2-h)/h = (h(4x + 2h - 1))/h = (cross(h)(4x + 2h - 1))/cross(h) = 4x +2h -1}}}