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Math Help - Slopes of Tangents - Help Please

  1. #1
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    Exclamation Slopes of Tangents - Help Please

    Hi there. So, I'm working on some pre-calc study, and Spring Break is coming up. I might not get a chance to work on this with my teacher, so I'm hoping that by posting this here, I might get an answer before I have to go back to school after Spring Break.

    So I'm working on finding slope equations for tangents of curves, used to find the rate of change at any given time. I believe this is still pre-calc, I am given such things as parabolas and y=x2 equations, and then I am supposed to find the slope of the tangent at any given point. I just got stuck on this question.

    What does the identity in a become when x=2? Question a asks for you to prove that 1/(x+h)2 - 1/x2 = -2xh - h2/ x2(x+h)2

    The slope of a chord is identified as y-step/x-step

    The answer to this question, as stated in the back of the book is [1/(2+h)2] - 1/4

    So how exactly do I get there? Do I just use the equation with x as 2? How do I find out what y equals when x is 2?
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  2. #2
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    Re: Slopes of Tangents - Help Please

    Quote Originally Posted by KaieraAi View Post
    What does the identity in a become when x=2? Question a asks for you to prove that 1/(x+h)2 - 1/x2 = -2xh - h2/ x2(x+h)2

    The slope of a chord is identified as y-step/x-step

    The answer to this question, as stated in the back of the book is [1/(2+h)2] - 1/4

    In the expression \frac{1}{(x+h)^2}-\frac{1}{x^2} replace x with 2 and do the algebra.
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  3. #3
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    Re: Slopes of Tangents - Help Please

    Quote Originally Posted by Plato View Post
    In the expression \frac{1}{(x+h)^2}-\frac{1}{x^2} replace x with 2 and do the algebra.
    I have simplified it down to \frac{h(h-4)}{4(h^2+4h+4)}
    Did I just simplify wrong?
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