Absolute value f interval?How would I find where the interval in which f increases and decreases in the following function. f ( x ) =∣ 4 − x 2 ∣What would I do find the zeroI know f ( x ) = { 4 − x 2 for | x | &lt; 2 x 2 − 4 for | x | &gt; 2 I suspect there are zeroes at 2 and -2 looking at the graph of the function. But how would find the zeroes.So that I can find the f interval.

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Absolute value f interval?How would I find where the interval in which f increases and decreases in the following function.  f  (  x  )  =∣  4  −      x    2    ∣What would I do find the zeroI know   f  (  x  )  =      {                            4          −                      x            2                              for                                |                    x                      |                    &amp;lt;          2                                                  x            2                    −          4                    for                                |                    x                      |                    &amp;gt;          2                        I suspect there are zeroes at 2 and -2 looking at the graph of the function. But how would find the zeroes.So that I can find the f interval.

Blaine Ross · Accepted Answer

Step 1The curve   y  =      |    4  −      x    2        |   is symmetric about the y-axis. So if we understand its behaviour for   x  ≥  0, we will know everything.We have       |    4  −      x    2        |    =  4  −      x    2   if       |    x      |    ≤  2, and       |    4  −      x    2        |    =      x    2    −  4 if       |    x      |    &amp;gt;  2.It is I think clear that   4  −      x    2   is decreasing in the interval [0,2]. It is also clear that       x    2    −  4 is increasing in the interval   [  2  ,  ∞  ]. erivatives can be used to show these things, but they are not necessary.Step 2So our function is decreasing in [0,2] and increasing in   [  2  ,  ∞  ).Now look at the reflection in the y-axis. We conclude that our function is decreasing in   (  −  ∞  ,  −  2  ] and increasing in [-2,0].

Skylar French · Accepted Answer

Step 1Look at the derivative:       f    ′    (  x  )  =      {                            −          2          x                    for                                |                    x                      |                    &amp;lt;          2                                      2          x                    for                                |                    x                      |                    &amp;gt;          2                      }  Step 2So f is decreasing in the intervalls   (  −  ∞  ,  −  2  ] and [0,2] and increasing in the intervalls [-2,0] and   [  2  ,  ∞  )

How would I find where the interval in which f increases and decreases in the following function. f(x)=|4-x^2|

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