# Identify the interval

• November 7th 2008, 03:39 PM
rowdy3
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
• November 7th 2008, 04:08 PM
mr fantastic
Quote:

Originally Posted by rowdy3
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.
• November 8th 2008, 12:06 AM
HallsofIvy
Quote:

Originally Posted by rowdy3
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.