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Thread: another trig tangent line equation

  1. #1
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    another trig tangent line equation

    So I have to find the equation of the tangent line then use the second derivative to see if the graph lies above or below the tangent line

    the function is

    $\displaystyle f(x) = x \sin 2x$ with a given x value of $\displaystyle x = \pi/4$ and so $\displaystyle f'(x) = \sin 2x + 2x \cos 2x $ and $\displaystyle f"(x) = 4(\cos 2x - x \sin 2x)$

    when I solve $\displaystyle f(\frac{\pi}{4}) = \frac{\pi}{4}$

    so this would just mean $\displaystyle y=x$ or I could say $\displaystyle \frac{\pi}{4} - y = \frac{\pi}{4} - x$

    correct?

    And the graph lies below the tangent line because solving because $\displaystyle f"(x) < 0$ as shown $\displaystyle f"(\frac{\pi}{4}) = - \pi$
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: another trig tangent line equation

    I think your answers are correct.
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