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Math Help - first derivatives test and trig functions

  1. #1
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    first derivatives test and trig functions

    I am supposed to use the first derivative test to find any local min/max of f(x)=sin^2(x)+cos)(x) on the interval \frac{\pi}{6},\frac{3\pi}{2}

    Take the derivative and get f'(x)=2cos(x)-sin(x)

    Set the derivative = 0 and I get 2cos(x)=sin(x)

    I graphed both 2cos(x) and sin(x) and there are 2 intersections. How do I solve for x?

    Thanks!
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  2. #2
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    Re: first derivatives test and trig functions

    Quote Originally Posted by baldysm View Post
    I am supposed to use the first derivative test to find any local min/max of f(x)=sin^2(x)+cos)(x) on the interval \frac{\pi}{6},\frac{3\pi}{2}
    Take the derivative and get \color{red}f'(x)=2cos(x)-sin(x)
    You have done the derivative incorrectly.

    f'(x)=2\sin(x)\cos(x)-\sin(x)
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  3. #3
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    Re: first derivatives test and trig functions

    Hey baldysm.

    Hint: sin(x)/cos(x) = tan(x).

    Edit: Also check HallsOfIvy's post above.
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