Lukecrayonz
  • Lukecrayonz
Difference quotient :) http://gyazo.com/892a400eceec44ef8f05e3ae87e1cdde
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
Lukecrayonz
  • Lukecrayonz
So I start out with -2(x+h)^2-(x+h)-2
Lukecrayonz
  • Lukecrayonz
Expand, simplify, and I get (-h-2 h^2-4 h x-4 x^2)/h
Lukecrayonz
  • Lukecrayonz
Luigi I know you know this

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Luigi0210
  • Luigi0210
I would help, but Siths is about to give a lecture
Lukecrayonz
  • Lukecrayonz
Good :D I need it haha
anonymous
  • anonymous
-2h^2-h-4hx-4x^2/h
anonymous
  • anonymous
simplified
anonymous
  • anonymous
\[f(x)=-2x^2-x-2~~\Rightarrow~~\begin{align*}f(x+h)&=-2(x+h)^2-(x+h)-2\\ &=-2(x^2+2xh+h^2)-x-h-2\\ &=-2x^2-2xh-2h^2-x-h-2 \end{align*}\] So the difference quotient becomes \[\begin{align*}\frac{f(x+h)-f(x)}{h}&=\frac{\left(-2x^2-2xh-2h^2-x-h-2\right)-\left(-2x^2-x-2\right)}{h}\\ &=\frac{-2xh-2h^2-h}{h} \end{align*}\]
Luigi0210
  • Luigi0210
^Told ya
anonymous
  • anonymous
:)
Lukecrayonz
  • Lukecrayonz
So then -2x-2h is my final answer?
Lukecrayonz
  • Lukecrayonz
Sith you can't leave btw, I'm borrowing you for about 30 minutes :D http://gyazo.com/e1df2303d768e488acc74aced45b31c7
Luigi0210
  • Luigi0210
Poor Siths :P
Lukecrayonz
  • Lukecrayonz
1992=5.5 1999=3.5
Lukecrayonz
  • Lukecrayonz
it's -0.286 right?
anonymous
  • anonymous
Should be \(-2x-2h-1\).
Lukecrayonz
  • Lukecrayonz
Oh right, dividing variables is to 1. Stupid me :O
anonymous
  • anonymous
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 \[\frac{f(b)-f(a)}{b-a}\]
anonymous
  • anonymous
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.
Lukecrayonz
  • Lukecrayonz
-3.5 for 1992-1999 6 for 2004-2007?
Lukecrayonz
  • Lukecrayonz
-6 sorry
anonymous
  • anonymous
\[\frac{3.5-5.5}{1999-1992}=\frac{-2}{7}\] \[\frac{1-1.5}{2007-2004}=\frac{-0.5}{3}=-6\]
Lukecrayonz
  • Lukecrayonz
Oh okay I had it right haha
Lukecrayonz
  • Lukecrayonz
BRB:-)

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