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Lena772

  • 2 years ago

(a) find an equation of the tangent line to the graph of at the given point, (b) use a graphing utility to graph the function and its tangent line at the point, and (c) use the derivative feature of the graphing utility to confirm your results.

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  1. Lena772
    • 2 years ago
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    function: y= cos 3x point: (pi/4, -sqrt2/2)

  2. ganeshie8
    • 2 years ago
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    where wer u stuck ?

  3. ganeshie8
    • 2 years ago
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    i saw u doing a similar problem the other day ? :)

  4. Decart
    • 2 years ago
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    take the derivative

  5. Lena772
    • 2 years ago
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    I just get confused when trig is added in

  6. Decart
    • 2 years ago
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    do you know what the derivative is

  7. Lena772
    • 2 years ago
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    dy/dx

  8. Decart
    • 2 years ago
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    -3sin3x

  9. Decart
    • 2 years ago
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    right

  10. Lena772
    • 2 years ago
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    yes

  11. ganeshie8
    • 2 years ago
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    so, slope = m = dy/dx = -3sin3x

  12. ganeshie8
    • 2 years ago
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    since u want the slope at point: (pi/4, -sqrt2/2) evaluate slope at x = pi/4

  13. ganeshie8
    • 2 years ago
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    dy/dx at x = pi/4 :- -3sin(3*pi/4) = ?

  14. Lena772
    • 2 years ago
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    -0.123

  15. Lena772
    • 2 years ago
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    @ganeshie8

  16. ganeshie8
    • 2 years ago
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    that doesnt look right you should get :- dy/dx at x = pi/4 :- -3sin(3*pi/4) = \(\large \frac{-3}{\sqrt{2}}\)

  17. ganeshie8
    • 2 years ago
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    now that u knw slope, m = \(\large \frac{-3}{\sqrt{2}}\) point: (pi/4, -sqrt2/2) wats the equation of tangent in point slope form ?

  18. Lena772
    • 2 years ago
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    y-(-sqrt2/3)=(-3/sqrt2)(x-(pi/4)

  19. Lena772
    • 2 years ago
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    ?

  20. Lena772
    • 2 years ago
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    @hartnn

  21. ganeshie8
    • 2 years ago
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    thats right !

  22. Lena772
    • 2 years ago
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    So that's for a? What would the graph look like for b? Do I just put that equation into Geogebra?

  23. Lena772
    • 2 years ago
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    @ganeshie8

  24. ganeshie8
    • 2 years ago
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    yup graph all 3 below :- 1) function: y= cos 3x 2) point: (pi/4, -sqrt2/2) 3) tangent : y-(-sqrt2/\(\color{red}{2}\))=(-3/sqrt2)(x-(pi/4)

  25. ganeshie8
    • 2 years ago
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    u should get exactly like the one attached

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