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Math Help - Finding the slope of the tangent

  1. #1
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    Finding the slope of the tangent

    y = x cosx

    How do I find when is the slope of the tangent equal to zero?
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  2. #2
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    Quote Originally Posted by looseenz2 View Post
    y = x cosx

    How do I find when is the slope of the tangent equal to zero?
    Solve  y' = 0

    Differentiate using the product rule
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  3. #3
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    Equivalently, the derivative is equal to 0.

    So, we calculate the derivative:

    \frac{d}{dx} x \cos x = -x \sin x + \cos x

    Then we set it equal to 0:

    \cos x - x \sin x = 0

    \cos x = x \sin x

    \frac{\cos x}{\sin x} = x

    \cot x = x
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  4. #4
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    So the answer would turn out to be tan x = \frac{1}{x}?
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  5. #5
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    Quote Originally Posted by looseenz2 View Post
    So the answer would turn out to be tan x = \frac{1}{x}?
    That's correct.
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  6. #6
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    Ahhh yay! Thank you
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