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cutie5507

  • 2 years ago

Find the slope of the tangent line to the curve sqrt(3x +3y) +sqrt(2xy) =11.5 at points (4,5)

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  1. cinar
    • 2 years ago
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    take the derivative and set it 0

  2. cutie5507
    • 2 years ago
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    im stuck on getting the deriviative

  3. cinar
    • 2 years ago
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    1/2(3x+3y)^(-1/2)(3+3y')+1/2(2xy)^(-1/2)(2y+2xy')=0

  4. cinar
    • 2 years ago
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    sub x=4 and y=5 find y'=m

  5. cinar
    • 2 years ago
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    after found m use this formula and write the eq. y-y1=m(x-x1) y1=5 x1=4

  6. cinar
    • 2 years ago
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    \[\frac{1}{2}(3x+3y)^{-1/2}(3+3y')+\frac{1}2 (2xy)^{-1/2}(2y+2xy')=0\]

  7. cutie5507
    • 2 years ago
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    i dont think im getting the right answer what did you get as the answer?

  8. cinar
    • 2 years ago
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    \[y'=m=\frac{4\sqrt{3}-2\sqrt{10}}{2\sqrt{10}-5\sqrt{3}}\]

  9. cinar
    • 2 years ago
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    use your cal..

  10. cinar
    • 2 years ago
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    -13/50 approx.

  11. cutie5507
    • 2 years ago
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    its showing as incorrect what was the exact answer?

  12. cinar
    • 2 years ago
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    what are the options..

  13. cutie5507
    • 2 years ago
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    i dont have options, but the assignment is online, so it tells me if he answer is correct or not

  14. cinar
    • 2 years ago
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    \[y=\frac{-13}{50}x+\frac{53}{10}\]

  15. cinar
    • 2 years ago
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    or \[y-4=(\frac{4\sqrt{3}-2\sqrt{10}}{2\sqrt{10}-5\sqrt{3}})(x-5)\]

  16. cinar
    • 2 years ago
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    is it saying round your answer or exact

  17. cutie5507
    • 2 years ago
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    exact

  18. cinar
    • 2 years ago
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    \[y=\frac{4\sqrt{3}-2\sqrt{10}}{2\sqrt{10}-5\sqrt{3}}x-5\frac{4\sqrt{3}-2\sqrt{10}}{2\sqrt{10}-5\sqrt{3}}+4\]

  19. cinar
    • 2 years ago
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    let me double check it

  20. cutie5507
    • 2 years ago
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    wht would the slope be?

  21. cinar
    • 2 years ago
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    \[y=-\frac{15\sqrt{2}+2\sqrt{15}}{12 \sqrt{2}+2\sqrt{15}}x+5\frac{15\sqrt{2}+2\sqrt{15}}{12 \sqrt{2}+2\sqrt{15}}+4\]

  22. cinar
    • 2 years ago
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    slope is coeff of x

  23. cutie5507
    • 2 years ago
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    its sill coming up as incorrect

  24. cinar
    • 2 years ago
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    \[y=-\frac{\sqrt{10}+4\sqrt{3}}{\sqrt{10}+4\sqrt{3}}x+5\frac{\sqrt{10}+4\sqrt{3}}{\sqrt{10}+4\sqrt{3}}+4\]

  25. cutie5507
    • 2 years ago
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    still coming up incorrect :/

  26. cinar
    • 2 years ago
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    \[y=\frac{-12\sqrt{3}+15}{2\sqrt{3}+12}x+\frac{60\sqrt{3}-75}{2\sqrt{3}+12}+4\]

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