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Math Help - Log Equation -Increasing and Decreasing Function

  1. #1
    mlg
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    Log Equation -Increasing and Decreasing Function

    I need help with this question:

    f(x) = sin(2x) + cos(2x) where x is an element of [0,pie].

    Find the interval on which this function is increasing and decreasing.

    I know that I must calculate f'(x) > 0 and f'(x) < 0

    But I'm not good at differentiating trigonometric functions and at finding the intervals.

    I would very grateful for any help.
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    Re: Log Equation -Increasing and Decreasing Function

    Quote Originally Posted by mlg View Post
    I need help with this question:
    f(x) = sin(2x) + cos(2x) where x is an element of [0,pie].
    Find the interval on which this function is increasing and decreasing.
    OH please, we eat pie but pi , \pi, is a Greek letter,

    \\f'(x)=2\cos(2x)-2\sin(2x)\\f''(x)=-4\sin(2x)-4\cos(2x)
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    mlg
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    Re: Log Equation -Increasing and Decreasing Function

    Thank you.
    I don't have the symbol 'pi' on my pc.
    How do I deal with 'pi' to follow on from here?
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    Re: Log Equation -Increasing and Decreasing Function

    Quote Originally Posted by mlg View Post
    Thank you.
    I don't have the symbol 'pi' on my pc.
    How do I deal with 'pi' to follow on from here?
    The point was the the correct spelling is pi not pie.
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    Re: Log Equation -Increasing and Decreasing Function

    Quote Originally Posted by mlg View Post
    Thank you.
    I don't have the symbol 'pi' on my pc.
    How do I deal with 'pi' to follow on from here?
    Find where the derivative is zero. You will get a list of x-coordinates. Put them in order from least to greatest. Then the intervals to check are (0,x_1), (x_1,x_2), ..., (x_k,\pi) for however many intervals there are. Plug one value from each interval into the derivative. That will tell you the sign of the derivative on each interval.
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  6. #6
    mlg
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    Re: Log Equation -Increasing and Decreasing Function

    Thanks.
    Could anyone give an example on how to work out one of these intervals.
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    Re: Log Equation -Increasing and Decreasing Function

    Example: Find where the derivative that Plato gave you is zero.
    Thanks from topsquark
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