increasing intervals decreasing interval

[rockinsnow]

suppose that a function f is increasing on the interval (0,5) decreasing on the interval (5,11) and has a value at x=5. what does the function value f(5) represent?

 

[MarkFL]

Have you drawn a sketch? This should make it pretty clear what is going on at x = 5.

 

[HallsofIvy]

That's a strange question. I'm not sure what you mean by "represent"! f(5) is, of course, the value of the function f(x) at x= 5. I have feeling that you are supposed to say that f(5) is a local maximum for the function, but unless f is continuous, which is not given, that is not true. For example, take f(x)= x for x< 4, x- 4, for x>= 5. Then f(5)= 1 but there exist values of x, arbitrarily close to 5, such that f(x)> 1. For example, f(4.9)= 4.9>1.