Question

Difference quotient :)
http://gyazo.com/892a400eceec44ef8f05e3ae87e1cdde

Answer 1

So I start out with -2(x+h)^2-(x+h)-2

Answer 2

Expand, simplify, and I get (-h-2 h^2-4 h x-4 x^2)/h

Answer 3

Luigi I know you know this

Answer 4

I would help, but Siths is about to give a lecture

Answer 5

Good :D I need it haha

Answer 6

-2h^2-h-4hx-4x^2/h

Answer 7

simplified

Answer 8

\[f(x)=-2x^2-x-2~~\Rightarrow~~\begin{align*}f(x+h)&=-2(x+h)^2-(x+h)-2\\
&=-2(x^2+2xh+h^2)-x-h-2\\
&=-2x^2-2xh-2h^2-x-h-2
\end{align*}\]
So the difference quotient becomes
\[\begin{align*}\frac{f(x+h)-f(x)}{h}&=\frac{\left(-2x^2-2xh-2h^2-x-h-2\right)-\left(-2x^2-x-2\right)}{h}\\
&=\frac{-2xh-2h^2-h}{h}
\end{align*}\]

Answer 9

^Told ya

Answer 10

:)

Answer 11

So then -2x-2h is my final answer?

Answer 12

Sith you can't leave btw, I'm borrowing you for about 30 minutes :D
http://gyazo.com/e1df2303d768e488acc74aced45b31c7

Answer 13

Poor Siths :P

Answer 14

1992=5.5
1999=3.5

Answer 15

it's -0.286 right?

Answer 16

Should be \(-2x-2h-1\).

Answer 17

Oh right, dividing variables is to 1. Stupid me :O

Answer 18

For the graph problem, you have to use a variation of the difference quotient. Average rate of change of a function \(f\) over some interval \([a,b]\) is given by
\[\frac{f(b)-f(a)}{b-a}\]

Answer 19

So for part A, \(a=1992\) and \(b=1999\), and it looks like \(f(a)=5.5\) and \(f(b)=3.5\).

For B, \(a=2004\) and \(b=2007\), and \(f(a)=1.5\) and \(f(b)=1\).

Plug in the values.

Answer 20

-3.5 for 1992-1999
6 for 2004-2007?

Answer 21

-6 sorry

Answer 22

\[\frac{3.5-5.5}{1999-1992}=\frac{-2}{7}\]
\[\frac{1-1.5}{2007-2004}=\frac{-0.5}{3}=-6\]

Answer 23

Oh okay I had it right haha

Answer 24

BRB:-)