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Math Help - local Extrema, Absolute Extrema, antiderivatives

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    local Extrema, Absolute Extrema, antiderivatives

    1)State the intervals on which f(x)=cos(x) - sin(x) is increasing and decreasing on the interval [- , ] , and name all the local extrema.

    (i don't know where to start on this problem.)

    ANSWER: Increasing on [-∏ , -∏/4) and (3∏/4]; decreasing on (-∏/4 , 3∏/4).
    Rel max (-∏/4 , √2) Rel min (3∏/4 , -√2).




    2) Find the absolute extrema of f(x)=sin(x) - cos(x) on the interval [0,∏]
    f'(x)=-cos(x) + sin(x)
    g(0)=0
    g(∏)=1
    This is where i'm stuck.

    ANSWER: Abs max √2 at x=3∏/4




    3) Use the given information to find f. f'(x)= 3x -x + 4 f(1)=2
    f(x)= x -x + 4x + c
    1 + - + 4 + c and f(1) = 2
    This is where i stopped. How did my professor get f(x) = x -x + 4x -5/2 ??

    ANSWER: f(x) = x -x + 4x - ⁵⁄₂





    Need Help! Thanks everyone!
    Last edited by Johnny Walker Black; November 18th 2009 at 09:09 PM.
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  2. #2
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    Quote Originally Posted by Johnny Walker Black View Post
    ...
    3) Use the given information to find f. f'(x)= 3x -x + 4 f(1)=2
    f(x)= x -x + 4x + c
    1 + - + 4 + c and f(1) = 2
    This is where i stopped. How did my professor get f(x) = x -x + 4x -5/2 ??

    ANSWER: f(x) = x -x + 4x - ⁵⁄₂
    From

    f(x)=x^3-\frac12 x^2+4x+c you'll get

    f(1)=2=1-\frac12+4+c~\implies~2=5-\frac12+c~\implies~2-5+\frac12 = c

    and you'll see that your prof is right.
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