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Noelaamaro

  • one year ago

I'm having trouble solving this question, can anyone help me? Find the equation of the tangent line at the given point. f(x)=csc(x) (8, csc(8))

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  1. Brittni0605
    • one year ago
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    Find the first derivative of your function. Then evaluate at your point.

  2. Noelaamaro
    • one year ago
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    I have my derivative = -csc(x) cot(x) Am I on the right track?

  3. Brittni0605
    • one year ago
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    Yes. -cotxcscx

  4. Noelaamaro
    • one year ago
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    Then plug in the x=8 and ill get the y-intercept right?

  5. Brittni0605
    • one year ago
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    Use point slope form.

  6. Brittni0605
    • one year ago
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    \[y-y_{1}=m(x-x_{1})\]

  7. Noelaamaro
    • one year ago
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    I've got y=-xcsc(x)cot(x)+8csc(x)cot(x)+csc(8) This doesn't seem right

  8. Brittni0605
    • one year ago
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    No, you need to find the slope at your point first. Do not plug any values into the form yet.

  9. Brittni0605
    • one year ago
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    \[f(x)=cscx\]

  10. Brittni0605
    • one year ago
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    \[f'(x)=-cotxcscx\]

  11. Brittni0605
    • one year ago
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    your point is (8, csc(8))...So..

  12. Brittni0605
    • one year ago
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    \[f'(8)= -\cot(8)\csc(8)\]

  13. Noelaamaro
    • one year ago
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    Sorry your last four messages say math processing error, can you input it again please

  14. Brittni0605
    • one year ago
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    \[y-y_{1}= (-\cot(8)\csc(8))(x-x_{1})\]

  15. Brittni0605
    • one year ago
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    f(x)=cscx f′(x)=−cotxcscx your point is (8, csc(8))...So.. f′(8)=−cot(8)csc(8) y−y1=(−cot(8)csc(8))(x−x1)

  16. Brittni0605
    • one year ago
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    y-csc(8)=(-cot(8)csc(8))(x-8) y=(-cot(8)csc(8)x)+8cot(8)csc(8)+csc(8)

  17. Noelaamaro
    • one year ago
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    Sorry I was working it out, nice to see I'm on the right track though so far

  18. Brittni0605
    • one year ago
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    Np.

  19. Noelaamaro
    • one year ago
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    I've got y=-51.12604x+416.19363

  20. Noelaamaro
    • one year ago
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    Thanks!

  21. robtobey
    • one year ago
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    A solution and plots using the Mathematica 9 Home Edition program is attached.

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