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bmelyk

Looking for someone to check my answer: Find an equation of the tangent line through the given point. x 2 y 3 + 15y = 34x, (3, 2)

  • one year ago
  • one year ago

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  1. bmelyk
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    \[\frac{ 34-2x }{ 2y+15 }\]

    • one year ago
  2. bmelyk
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    thats the answer i got.

    • one year ago
  3. bmelyk
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    well that's what i had for y'

    • one year ago
  4. asnaseer
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    You first need to use implicit differentiation to find an expression for \(\displaystyle\frac{dy}{dx}\). Then substitute x=3 and y=2 into that expression to get the slope of the tangent line at that point. So then you will know the slope of the tangent line and you also know it passes through the point (3,2) - use this information to calculate the equation of the tangent line.

    • one year ago
  5. bmelyk
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    was my y' equation correct?

    • one year ago
  6. asnaseer
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    it doesn't look correct to me - can you please list your steps so that I can help spot where you may have made a mistake?

    • one year ago
  7. bmelyk
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    \[x ^{2}y ^{2}+15y=34x\] \[2x*2yy'+15y'=34\] \[y'(2y+15)=34-2x\] \[y'=\frac{ 34-2x }{ 2y+15 }\]

    • one year ago
  8. asnaseer
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    I thought you had \(y^3\) in the equation listed in your question?

    • one year ago
  9. bmelyk
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    lol so it is.

    • one year ago
  10. bmelyk
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    \[y'=\frac{ 34-2x }{ 3y ^{2}+15 }\]

    • one year ago
  11. bmelyk
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    did i have it right the second time (right above what you just wrote)

    • one year ago
  12. asnaseer
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    sorry I meant:\[\frac{d}{dx}(x^2y^3)=(x^2)\frac{d}{dx}(y^3)+y^3\frac{d}{dx}(x^2)\]

    • one year ago
  13. asnaseer
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    you haven't used the chain rule correctly

    • one year ago
  14. asnaseer
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    I mean "product rule"

    • one year ago
  15. asnaseer
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    have a look here: http://www.1728.org/chainrul.htm

    • one year ago
  16. bmelyk
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    \[x ^{2}*3y ^{2}y'+y ^{3}2x+15y'=34\]

    • one year ago
  17. asnaseer
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    that is correct :)

    • one year ago
  18. bmelyk
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    okay so now i isolate y'

    • one year ago
  19. asnaseer
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    exactly

    • one year ago
  20. bmelyk
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    \[y'=\frac{ 34-2xy ^{3} }{ x ^{2}3y ^{2}+15 }\]

    • one year ago
  21. asnaseer
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    yup - now follow the other steps that I had listed above.

    • one year ago
  22. asnaseer
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    NOTE: we don't usually write an expression as \(x^23y^2\) - it is better to write it as \(3x^2y^2\)

    • one year ago
  23. bmelyk
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    ok.

    • one year ago
  24. asnaseer
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    the general rule of thumb is to write in this order: 1. Constants first 2. Then letters in alphabetical order

    • one year ago
  25. bmelyk
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    okay so now i sub in my points right?

    • one year ago
  26. asnaseer
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    correct

    • one year ago
  27. bmelyk
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    so i had: -14/123

    • one year ago
  28. asnaseer
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    perfect! just a couple of more steps to go now :)

    • one year ago
  29. bmelyk
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    is the equation: \[y-2=-14/123x+42/123\]

    • one year ago
  30. asnaseer
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    yes - that looks correct. I wouldn't have separated the two constants here (the -2 and the 42/123)

    • one year ago
  31. asnaseer
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    you may also want to multiply both sides by 123 to remove the fractions from the final equation.

    • one year ago
  32. bmelyk
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    so how would you make it look?

    • one year ago
  33. asnaseer
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    ok, you got to this equation:\[y-2=-14/123x+42/123\]first add 2 to both sides to get:\[y=-14x/123 + 288/123\]then multiply both sides by 123 - what will you get then?

    • one year ago
  34. bmelyk
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    y123=-14x+288

    • one year ago
  35. asnaseer
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    correct - but again, remember to write constants first - so 123y instead of y123

    • one year ago
  36. bmelyk
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    that's not really how you write the equation of a line though.

    • one year ago
  37. asnaseer
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    so I would write the final equation as:\[123y=288-14x\]

    • one year ago
  38. asnaseer
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    it is still an equation of a line. you can write it in "standard form" as follows:\[14x+123y=288\]

    • one year ago
  39. asnaseer
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    maybe you are only used to seeing it in the form: \(y=mx +c\)

    • one year ago
  40. asnaseer
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    One last advice before I leave - you wrote one of the terms in your original equation as: -14/123x this can sometimes be confused for: \[-\frac{14}{123x}\]so it is usually better to write it as: -14x/123

    • one year ago
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