# Simple question

1. Aug 9, 2011

### fmdk

Given a simple equation y = y (t), where does maximum occur.

I am thinking that this is an asymptote?

is this a correct assumption?

2. Aug 9, 2011

### Staff: Mentor

Without knowing the formula for your function, it is impossible to know where a maximum occurs or whether the function has an asymptote of any kind.

3. Aug 9, 2011

### fmdk

This was the only information that i was provided with on the question sheet.

4. Aug 9, 2011

### Staff: Mentor

Was there a graph included with the problem?
In general, a maximum or minimum can occur at any of three places:
1) a point where the derivative is zero.
2) a point in the domain of the function at which the derivative is undefined.
3) an endpoint of the domain of the function.

5. Aug 9, 2011

### fmdk

actually this was all the information that was giving for this particular question.

6. Aug 9, 2011

### Char. Limit

Well, firstly, what dictates a maximum? We know that for it to be a maximum, the slope at that point must be zero, so y'(t)=0. And furthermore, we know that the second derivative of y must be negative, so y''(t)<0. So the maximum is every point satisfying those two conditions.

EDIT: Note that I am assuming that y(t) is continuous over the whole real line.

7. Aug 9, 2011

### Bohrok

y = -|x| isn't differentiable at its maximum.

Edit: I see Mark basically mentioned this in 2) in his last post.

8. Aug 9, 2011

### Char. Limit

Ah, touche. Let me revise my earlier statement to say that we assume y(t) AND y'(t) are continuous over the whole real line.