# What is different between critical point and inflection point?

There seem to be two definitions of "critical point" in use. But with that in mind:

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A critical point is a point on the graph of a function where its derivative is either zero or undefined. It indicates a potential location for a maximum, minimum, or saddle point.

An inflection point, on the other hand, is a point on the graph of a function where the concavity changes. It is where the second derivative of the function changes sign, indicating a change in the direction of curvature of the graph.

In summary, a critical point relates to the behavior of the first derivative of a function, indicating possible extrema, while an inflection point relates to the behavior of the second derivative, indicating where the curvature of the function changes.

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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.

- Find y′′ for the curve ln(x) + y = ln(x^2) − y^2 at y = 0? Note that the domain for x is that x > 0. There will only be one point on the curve with y = 0
- For what values of x is #f(x)=3x^3-7x^2-5x+9# concave or convex?
- How would you find the inflection point and the concavity of #g(x) = (5x - 2.6) / (5x - 6.76)^2#? I know I have to take the 2nd derivative but i'm not sure how because of the odd way this function is set up.?
- What are the points of inflection of #f(x)=x/(1+x^2)#?
- How do you sketch the curve #y=e^x-sinx# by finding local maximum, minimum, inflection points, asymptotes, and intercepts?

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