- #1

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I am thinking that this is an asymptote?

is this a correct assumption?

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- Thread starter fmdk
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- #1

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I am thinking that this is an asymptote?

is this a correct assumption?

- #2

Mark44

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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.

I am thinking that this is an asymptote?

is this a correct assumption?

- #3

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

- #4

Mark44

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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

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

- #6

Char. Limit

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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.

- #7

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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.

- #8

Char. Limit

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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.

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