# Simple question

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

I am thinking that this is an asymptote?

is this a correct assumption?

## Answers and Replies

Mark44
Mentor
Given a simple equation y = y (t), where does maximum occur.

I am thinking that this is an asymptote?

is this a correct assumption?
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.

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

Mark44
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.

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

Char. Limit
Gold Member
Given a simple equation y = y (t), where does maximum occur.

I am thinking that this is an asymptote?

is this a correct assumption?

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.

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.

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

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

Char. Limit
Gold Member
y = -|x| isn't differentiable at its maximum.

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.