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anonymous

  • 5 years ago

the equation of the line tangent to the curve y=kx+8/k+x at x= -2 is y=x+4. what is the value of k?

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  1. anonymous
    • 5 years ago
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    check your question , possibly a typo

  2. anonymous
    • 5 years ago
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    no, thats it word for word

  3. anonymous
    • 5 years ago
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    y= (k+1)x +(8/k) ( eqn of the "curve" , even though its a line )

  4. anonymous
    • 5 years ago
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    the only way to have a tangent to a line , is for the tangent to be the line

  5. anonymous
    • 5 years ago
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    so (k+1)x +(8/k) = x+4

  6. anonymous
    • 5 years ago
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    now we are told they are a tangent at x=-2, so we could sub x=-2 into the above to find k , but we could also sub any value of x we like , these lines have to be the same for all x

  7. anonymous
    • 5 years ago
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    but ill just sub x=-2 -2(k+1) + 8/k = 2 -2k(k+1) +8 = 2k -2k^2 -2k -2k +8 =0 -2k^2 -4k+8 =0 -2(k^2 +2k -4) =0

  8. anonymous
    • 5 years ago
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    k^2 +2k -4 =0

  9. anonymous
    • 5 years ago
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    how did you get that function?

  10. anonymous
    • 5 years ago
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    (k+1)^2 = 5 k +1 = +-sqrt(5) k = -1+-sqrt(5)

  11. anonymous
    • 5 years ago
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    not an answer

  12. anonymous
    • 5 years ago
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    well your teacher is stupid

  13. anonymous
    • 5 years ago
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    i doubt that you dont even know what the equation of the line tangent is

  14. anonymous
    • 5 years ago
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    this is a question from an ap test so there are no typos

  15. anonymous
    • 5 years ago
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    lol was the curve \[y=kx + \frac{8}{k+x}\] y =

  16. anonymous
    • 5 years ago
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    if it was................ :|

  17. anonymous
    • 5 years ago
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    use brackets when you are writting fractions on the net :|

  18. anonymous
    • 5 years ago
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    put the kx on top also

  19. anonymous
    • 5 years ago
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    sorry? didnt know

  20. anonymous
    • 5 years ago
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    lol

  21. anonymous
    • 5 years ago
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    y=(kx+8)/k+x

  22. anonymous
    • 5 years ago
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    With the given info, one finds the tangent vector of the curve to be <1, -1> and the point of tangency to be (-2, 2). You can find k by plugging in (-2, 2).

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spraguer (Moderator)
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