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anonymous

  • 5 years ago

how do u find the equation of the tangent line to the curve at the given point: y=e^x/x, (1,e)

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  1. anonymous
    • 5 years ago
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    1. Take its derivative: \[dy/dx = -e ^{x}/x ^{2} + e ^{x}/x\]

  2. anonymous
    • 5 years ago
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    Substitute x = 1

  3. anonymous
    • 5 years ago
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    Whatever value you obtain for dy/dx after the substitution, let that represent your m value for the equation y = mx+c

  4. anonymous
    • 5 years ago
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    i got 0 as the slope but then when i plug it in i still get the wrong answer

  5. anonymous
    • 5 years ago
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    To solve for the constant 'c', just substitute: x = 1 y = e m =dy/dx (Its numerical value that you obtained) Then, for your final sub in the c and m values

  6. anonymous
    • 5 years ago
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    Double check to make sure my derivative is correct

  7. anonymous
    • 5 years ago
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    But i'm quite sure the steps are correct though.

  8. anonymous
    • 5 years ago
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    ok i got it thanks

  9. anonymous
    • 5 years ago
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    Using the derivative presented above, I also get 0 as it's derivative at x=1. If this is the case then the equation of the tangent line at the point (1,e) on the original curve should be y=e.

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