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Math Help - Identify the interval

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    Identify the interval

    Identify the interval on which the function F(x)= 4 - x^2 is increasing or decreasing. Write your answer using interval notation.
    My answer was decreasing: (-infinity to infinity) and increasing: (0 to infinity). It was marked wrong. How do I do this problem?
    Thanks
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    Quote Originally Posted by rowdy3 View Post
    Identify the interval on which the function F(x)= 4 - x^2 is increasing or decreasing. Write your answer using interval notation.
    My answer was decreasing: (-infinity to infinity) and increasing: (0 to infinity).

    Mr F says: How can it be increasing AND decreasing over (0 to infinity). Surely you meant decreasing for (-infinity to 0) which is still wrong but at least it's not wrong because of inconsistency.

    It was marked wrong. How do I do this problem?
    Thanks
    Increasing for \frac{dF}{dx} > 0. Solve for x.
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    Quote Originally Posted by rowdy3 View Post
    Identify the interval on which the function F(x)= 4 - x^2 is increasing or decreasing. Write your answer using interval notation.
    My answer was decreasing: (-infinity to infinity) and increasing: (0 to infinity). It was marked wrong. How do I do this problem?
    Thanks
    Surely it should be obvious that the function cannot be both increasing and decreasing on (0 to infinity)! Did you mean "decreasing on (-\infty, 0) and increasing on (0, \infty)"?

    That's not correct because the graph of y= 4- x^2 is a parabola that opens downward. f(x) is increasing for x< 0 and decreasing for x> 0.
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