Question 1152207


if {{{f(x)= x^2 - 2x+7}}}, 

find {{{f(x+h)- f(x)}}}

first:

{{{f(x+h)=(x+h)^2 - 2(x+h)+7}}}

{{{f(x+h)=x^2+2xh+h^2 - 2x-2h+7}}}

then

{{{f(x+h)- f(x)=x^2+2xh+h^2 - 2x-2h+7-(x^2 - 2x+7)}}}

{{{f(x+h)- f(x)=x^2+2xh+h^2 - 2x-2h+7-x^2 +2x-7}}}....simplify

{{{f(x+h)- f(x)=cross(x^2)+2xh+h^2 -cross( 2x)-2h+cross(7)-cross(x^2) +cross( 2x)-cross(7)}}}

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