my hairs are falling off and i still can't do this..

Test Preparation
1

<p>difference quotient</p>

<p>f(x+h)-f(x)/h</p>

<p>what is the f(x)=x^2</p>

<p>the answer is 2x+h</p>

<p>i did X^2+h - (X^2)/h</p>

<p>i have no idea where 2X+h comes from</p>

2

<p>If f(x) = x^2, f(x+h) = (x+h)^2 = x^2 + 2x + h
Then, f(x+h) - f(x) = x^2 + 2x + h - x^2 = 2x + h</p>

<p>...and that's where the 2x+h comes from :) .</p>

<p>( Hang on to your hair, it gets harder & harder to come by once you pass 50. Trust me on this one...)</p>

3

<p>thanks but what i dont get is isnt (x+h)^2 = (x+h)(x+h) which is X^2 +2xh+h^2?</p>

4

<p>Oops, my typo. It should be</p>

<p>[f(x+h) - f(x)] / h = [2xh + h^2] / h = 2x + h</p>

5

<p>you can hit me if you want
but it stil doesn't make sense
you said [f(x+h) - f(x)] / h = [2xh + h^2] / h
shouldnt [2xh + h^2] / h = 2x+h^2 instead of 2x+h?</p>

6

<p>Oy...
[2xh + h^2] / h means you divide each & every one of additive terms in the numerator by h; so
[2xh + h^2] / h = (2xh/h) + (h^2 / h) = 2x + h .</p>

<p>(Try it with numbers instead; what is (20 + 32) / 4 ? It's not 20 + (32/4), but instead (20/4) + (32/4) ).</p>

7

<p>f(x)=x^2</p>

<p>[f(x+h)-f(x)] / h</p>

<p>[(x+h)^2 - x^2] / h</p>

<p>[x^2 + 2xh + h^2 - x^2] / h</p>

<p>[ 2xh + h^2] / h</p>

<p>[h(2x+h)]/h</p>

<p>2x+h</p>

<p>EDIT: Late here, so don't mind my post. :)</p>

8

<p>i got it...
miracle!
haha thanks everybody!</p>