Where Does Maximum Occur in y = y(t) Equation?

[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?

 

[Mark44]

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.

 

[fmdk]

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

 

[Mark44]

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.

 

[fmdk]

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

 

[Char. Limit]

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.

 

[Bohrok]

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]

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.