Results 1 to 6 of 6

Math Help - Average rate of change

  1. #1
    Newbie
    Joined
    Sep 2012
    From
    Maryland
    Posts
    15

    Average rate of change

    Here's the problem: A function is given below. Determine the average rate of change of the function between x = -2 and x = -2 + h.

    So what I did was g(-2)= -(5/-2)=5/2
    g(-2+h)=-(5/-2+h)= (would this be 5/2+h)

    I did this problem a couple of different ways ( I changed around what I thought g(-2+h) would equal) and I have a bunch of different answers. I was wondering if someone could give me the correct answer and explain what they did. Thank you.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Sep 2012
    From
    Planet Earth
    Posts
    195
    Thanks
    49

    Re: Average rate of change

    Average rate of change is how much the function changed divided by how much x changed.

    = \frac{g(-2 + h) - g(-2)}{h}

    = \frac{\frac{-5}{h-2} - 2.5}{h}

    = \frac{-5}{h(h-2)} - \frac{2.5}{h}

    = \frac{-5}{h(h-2)} - \frac{2.5(h-2)}{h(h-2)}

    = \frac{-5 - 2.5h + 5}{h(h-2)}

    = \frac{-2.5}{h-2} = \frac{5}{4-2h}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2012
    From
    Maryland
    Posts
    15

    Re: Average rate of change

    Do you factor out the bottom? 2(2-h)
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Average rate of change

    The average rate of change is given by the difference quotient:

    \frac{g(x+h)-g(x)}{h}=\frac{\left(-\frac{5}{x+h} \right)-\left(-\frac{5}{x} \right)}{h}=\frac{-\frac{5}{x+h}+\frac{5}{x}}{h}=

    \frac{5(x+h)-5x}{hx(x+h)}=\frac{5h}{hx(x+h)}=\frac{5}{x(x+h)}

    Now, plug in -2 for x to get:

    \frac{5}{(-2)((-2)+h)}=\frac{5}{2(2-h)}
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Sep 2012
    From
    Planet Earth
    Posts
    195
    Thanks
    49

    Re: Average rate of change

    I made a common denominator and then I removed an h from both the numerator and denominator after simplifying. Is there a step you want me to clarify?

    Edit: if you mean the last step, then I expanded the denominator. 2(2-h) = 4-2h
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Sep 2012
    From
    Maryland
    Posts
    15

    Re: Average rate of change

    Thank you for your help. This is one of the answers I came up with, so I'm glad to know I was doing something right.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Help with average rate of change
    Posted in the Pre-Calculus Forum
    Replies: 7
    Last Post: January 14th 2011, 11:53 AM
  2. Average Rate of Change
    Posted in the Calculus Forum
    Replies: 3
    Last Post: July 13th 2010, 01:59 PM
  3. Average rate of change!
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: January 27th 2010, 07:32 PM
  4. average rate of change? help
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: January 29th 2009, 09:19 PM
  5. average rate of change
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: August 16th 2008, 09:55 AM

Search Tags


/mathhelpforum @mathhelpforum