Question 966469


If {{{f(x) = x(x+2)}}}, find {{{(f(x+h)-f(x-h))/2h}}}

first find
{{{f(x+h)=(x+h)((x+h)+2)=(x+h)(x+h+2)=h^2+2hx+2h+x^2+2x}}}
{{{f(x-h)=(x-h)((x-h)+2)=(x-h)(x-h+2)=h^2-2hx-2h+x^2+2x}}}

then you have:

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

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

{{{(f(x+h)-f(x-h))/2h=(4hx+4h)/2h}}}

{{{(f(x+h)-f(x-h))/2h=4h(x+1)/2h}}}

{{{(f(x+h)-f(x-h))/2h=2(x+1)}}}