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Math Help - Slope of a Curve

  1. #1
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    Slope of a Curve

    Let f(x) be the function . Then the quotient can be simplified to for: a= _____ & b= _____
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    Re: Slope of a Curve

    Quote Originally Posted by spyder12 View Post
    Let f(x) be the function . Then the quotient can be simplified to for: a= _____ & b= _____
    Can you do the algebra?

    \frac{\frac{1}{h+16}-\frac{1}{16}}{h}=~?
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    Re: Slope of a Curve

    f(6+h)=\frac{1}{(6+h)+10}=\frac{1}{h+16}

    f(6)=\frac{1}{(6)+10}=\frac{1}{16}

    Now, putting these into the quotient gives you what?
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  4. #4
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    Re: Slope of a Curve

    ok so then that equals (1/h) / h right? then what do i do
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    Re: Slope of a Curve

    Quote Originally Posted by spyder12 View Post
    ok so then that equals (1/h) / h right? then what do i do
    \frac{\frac{1}{h+16} - \frac{1}{16}}{h} \ne \frac{\frac{1}{h}}{h}

    you first need to combine the fractions in the numerator using the common denominator 16(h+16)
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  6. #6
    MHF Contributor MarkFL's Avatar
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    Re: Slope of a Curve

    No, how did you get that?
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    Re: Slope of a Curve

    Quote Originally Posted by MarkFL2 View Post
    No, how did you get that?
    methinks some creative algebra ...

    \frac{1}{h+16} = \frac{1}{h} + \frac{1}{16}

    ... which, of course, is incorrect.
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  8. #8
    MHF Contributor MarkFL's Avatar
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    Re: Slope of a Curve

    That was my inclination as well...many folks make this kind of error.
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  9. #9
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    Re: Slope of a Curve

    alright so then ( (1) / 16(h+16) ) / h = ( (1) / (16h+265) ) / h = (16h+256)^-1 / h , so to answer my question a= 16 & b=256
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  10. #10
    MHF Contributor MarkFL's Avatar
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    Re: Slope of a Curve

    Yes, good work!
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  11. #11
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    Re: Slope of a Curve

    alright so then ( (1) / 16(h+16) ) / h = ( (1) / (16h+265) ) / h = (16h+256)^-1 / h , so to answer my question a= 16 & b=256
    you may have "stumbled" onto the correct constants, but this is incorrect

    \frac{1}{h} \left(\frac{1}{h+16} - \frac{1}{16}\right)

    \frac{1}{h} \left(\frac{16}{16(h+16)} - \frac{h+16}{16(h+16)}\right)

    \frac{1}{h} \left(\frac{16 - h - 16}{16(h+16)}\right)

    \frac{1}{h} \left(\frac{ -h}{16(h+16)}\right)

    \frac{ -1}{16(h+16)}\right) = \frac{-1}{16h + 256}
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  12. #12
    MHF Contributor MarkFL's Avatar
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    Re: Slope of a Curve

    Good catch, I only looked at the end result.
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