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Math Help - Tangent Line Prob 2

  1. #1
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    Tangent Line Prob 2

    Last calc question, I swear. This is my last question for the night.

    For the given function, find the points on the graph at which the tangent line has slope 1.

    y = 1/3x^3 - 1/2x^2 +x
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by aphan19 View Post
    Last calc question, I swear. This is my last question for the night.

    For the given function, find the points on the graph at which the tangent line has slope 1.

    y = 1/3x^3 - 1/2x^2 +x
    Tangent lines slope at x_0=f'(x_0) where f(x) is the curve the tangent line is tangent to...so find

    x such that f'(x)=x^2-x+1=1
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  3. #3
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by aphan19 View Post
    Last calc question, I swear. This is my last question for the night.

    For the given function, find the points on the graph at which the tangent line has slope 1.

    y = 1/3x^3 - 1/2x^2 +x

    Find y'.

    y^{/}=x^2-x+1

    Set it equal to 1 to find the x values at which the derivative is equal to one:


    1=x^2-x+1 when x^2-x=0\rightarrow x(x-1)=0 \rightarrow x=0 or x=1.

    Hope that answered your question!
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    Why is it when I take the derivative of 1/3x^3 its x^2? I thought I was suppose to move the x^3 to the top making it x^-3?
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  5. #5
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by aphan19 View Post
    Why is it when I take the derivative of 1/3x^3 its x^2? I thought I was suppose to move the x^3 to the top making it x^-3?
    So did you mean \frac{1}{3x^3} or \frac{1}{3}x^3?
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    Nvm, I got it. thank you very much though.
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  7. #7
    Rhymes with Orange Chris L T521's Avatar
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    If you mean y=\frac{1}{3x^3}-\frac{1}{2x^2}+x, the derivative would then be y^{/}=-\frac{1}{x^4}+\frac{1}{x^3}+1. To see where it's equal to 1:

    1=-\frac{1}{x^4}+\frac{1}{x^3}+1

    Multiply through by x^4 to clean this up:


    x^4=-1+x+x^4\rightarrow x=1. Is this what you're looking for?
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  8. #8
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by aphan19 View Post
    Nvm, I got it. thank you very much though.
    Ok. I ended up working out the other problem...you can ignore that...if you want
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  9. #9
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Chris L T521 View Post
    Ok. I ended up working out the other problem...you can ignore that...if you want
    You uhm...might want to wait until they respond to your question before you go ahead and asnwer it possibly confusing them
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  10. #10
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Mathstud28 View Post
    You uhm...might want to wait until they respond to your question before you go ahead and asnwer it possibly confusing them
    Yea. Thanks for that. I should have waited.
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  11. #11
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Chris L T521 View Post
    Yea. Thanks for that. I should have waited.
    Don't worry! I applaud your enthusiasm!
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