Monday, August 24, 2009

#73-80 on homework of 8/24

I was doing fine until I got to these problems. I don't know if I over-mathed myself or if I'm just super slow. I completely lost where I was going with any of them. I even lost how to begin. I can't even get to where Kait got. Can someone re-explain how to do one of those problems in simple terms? Please and thank you!!
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3 comments:

  1. XxDohxXAugust 25, 2009 at 7:29 AM

    Let's look at the first one, for example.

    We have
    x^2
    --------------
    x-1

    To start to solve this, we have to know what we are looking for. We are looking for horizontal tangent lines. A horizontal tangent line is one that only "runs", right? No rise. So 0/something. 0 over anything is always 0. So we know that we need to find the points on this curve where the slope at that point is 0.

    To do this, take the derivative. We take the derivative with the quotient rule and get...

    (x-1)2x-(x^2)
    ----------------------
    (x-1)^2

    Now we know that equation describes slope. If we would plug in an x, we would get the slope at the point. But we don't have our x's...and we KNOW our slope already, 0.

    So set that equal to 0 and solve. When you set it equal to 0, you get rid of the bottom first. Multiply both sides by the bottom to cancel it out on the left side, and when you do 0 times x-1 squared, it just is 0. Now you have 2x(x-1)-x^2. Simplify this to x^2-2x and set it equal to 0. Now solve for x.

    x(x-2)=0
    x=0 and x=2

    Now we have our x values, but we need a point. So we take these and plug this into our original to get the points (0,0) and (2,4).


    Hope this helps someone. :-)

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  2. tlt2010August 25, 2009 at 4:18 PM

    i hope i'm doing this right but for #75 i used the product rule and got

    4(x^2)-(4x-2)(2x)
    ------------------
    (x^2)^2

    now you take the derivitive, which i got

    -4x^2-4x
    ---------
    (x^2)^2

    and i took out an x
    now we have to set that equal to zero
    times both sides by x^2 to then your left with
    x^2(-4x-4)=0

    x=0 and x=-1

    now we plug in those points to get our other points

    so we get (0,-2) and (-1,-3)

    hopefully this helps

    ReplyDelete
  3. ArchimedesAugust 25, 2009 at 4:20 PM

    It is the quotient rule..

    ReplyDelete

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