Is 8 a Relative Max of F in the Given Domain?

[rpc]

In class today we were doing a problem where we were given the graph of f (the derivitive of F).

The domain was -3<x < or = 8

f(8)=0 and f had changed from positive <8 to 0, indicating a probable relative max (the function looked like a sinusoid, but the points after 8 were not graphed or included in the domain)

Therefore my question is, is 8 a relative max of F in that domain? or is not enough info there (i.e. it could have just bounced)?

My reasoning for it being a rel max is that it is a max value in the window.

What do you think?

 

[HallsofIvy]

It is a relative maximum IN THAT DOMAIN. As long as the domain of F is -3 to 8, what happens for x> 8 is irrelevant: NOTHING happens because F is not defined for x> 8.

 

[M98Ranger]

Based on the given information, it is not possible to determine if 8 is a relative max of F in the given domain. While it is true that f(8)=0 and the function appears to have a sinusoidal shape, it is not clear if the graph continues beyond the given domain of -3<x<or=8. If the function continues to decrease after x=8, then 8 would not be a relative max. However, if the function remains at 0 or starts to increase after x=8, then 8 could be a relative max. Therefore, without knowing the behavior of the function beyond the given domain, it is not possible to determine if 8 is a relative max or not. It is important to have all the necessary information and a complete understanding of the function in order to determine if a value is a relative max or not.