# Can an asymptote be an inflection point?

Since an inflection point is a point on an equation, I assume you mean

"Can an asymptote intersect the line of an equation at an inflection point?"

Under current/modern usage of the concept of asymptote, the answer is a simple "yes";

for example,

Older, more traditional definitions of "asymptote" included a restriction that the equation could not cross the asymptote infinitely; so the given example would not be valid.

However it is possible to imagine a situation like that pictured below

which would still be valid under traditional definitions:

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As Alan P. said in his answer, a graph can have a point of inflection that lies on its asymptote.

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No, an asymptote cannot be an inflection point. An inflection point is where a curve changes concavity, from concave up to concave down or vice versa, and it occurs at a specific point on the curve. An asymptote, on the other hand, is a line that the curve approaches but never actually reaches, serving as a boundary behavior for the curve at infinity or at points of discontinuity.

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No, an asymptote cannot be an inflection point. Asymptotes describe the behavior of a curve as it approaches a certain value, typically as the independent variable approaches positive or negative infinity. Inflection points, on the other hand, occur where the concavity of a curve changes. An inflection point is characterized by a change in the direction of the curve's curvature. These two concepts describe fundamentally different aspects of a function's behavior and do not coincide.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- For what values of x is #f(x)= -x^3+3x^2-2x+2 # concave or convex?
- How do you determine whether the function #f^('')(x) = 36x^2-12# is concave up or concave down and its intervals?
- What are the points of inflection, if any, of #f(x)=x^(1/3) #?
- What is the second derivative of #f(x)= ln sqrt(3x-7)#?
- What are the points of inflection, if any, of #f(x)=2x^3 + 8x^2 #?

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