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Math Help - determine slope of y=2x^2 - 4x + 2

  1. #1
    apm
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    determine slope of y=2x^2 - 4x + 2

    i have to determine the slope of y=2x^2 - 4x +2

    isn't that a parabola? how can it have a slope or does it have two different ones? but how can a curve have a slope?

    there is also another problem similar to this
    y=x^2 from (-1,1) to (x,y) and it wants me to determine change in y/change in x in terms of x

    Thanks!
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    apm
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    thank you
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    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by apm View Post
    i have to determine the slope of y=2x^2 - 4x +2

    isn't that a parabola? how can it have a slope or does it have two different ones? but how can a curve have a slope?
    If we were to look for a tangent line, we end up differentiating the function. This gives us the slope of the function. However, the function has an infinite number of slopes, unless a particular x value is specified.

    In our case, y=2x^2-4x+2.

    When we differentiate it, we get y'=4x-4

    This is our slope. Since there is no x value specified, there are an infinite number of slopes values that depend on the value of x, where x\in\mathbb{R}.

    there is also another problem similar to this
    y=x^2 from (-1,1) to (x,y) and it wants me to determine change in y/change in x in terms of x

    Thanks!
    I would assume that they are requesting the average slope...

    The line is defined over the interval (-1,x_0)

    Thus, \frac{\Delta y}{\Delta x}=\frac{f(b)-f(a)}{b-a}\implies \frac{\Delta y}{\Delta x}=\frac{x_0^2-1}{x_0+1}\implies\color{red}\boxed{\frac{\Delta y}{\Delta x}=x_0-1}

    I hope this makes sense.

    --Chris
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    Sorry for posting in a kind-of-old thread, but I have the same problem and I can't figure it out. The posted problem does not give a particular point to find the slope of.

    Are there any examples of solving such problems, step by step and preferably with explanations?

    p.s! I hope its not too difficult to understand what I just typed, my first language has loose word order and I just spent half a day translating to that. :P

    e: Thanks to mr. fantastic for rewording my post. I got . What will happen to 2h?
    Last edited by KSiimson; January 31st 2009 at 11:27 PM. Reason: So that it means sense. The post looked like it had been moved - it had a link to this thread ....?
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