# What do points of inflection represent on a graph?

Inflection points are the points on the graph at which the concavity of the graph changes.

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Points of inflection on a graph represent locations where the curvature of the graph changes direction. Specifically, at a point of inflection, the concavity of the curve changes from concave upwards to concave downwards, or vice versa. These points indicate significant changes in the rate of change or the behavior of the function being graphed.

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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.

- What are the points of inflection, if any, of #f(x)= x^3 + 9x^2 + 15x - 25 #?
- How do you use the first and second derivatives to sketch #f(x) = sqrt(4 - x^2)#?
- How do you find the first and second derivative of #(lnx)/x^2#?
- What is the second derivative of #f(x)=(e^x + e^-x) / 2 #?
- What is the second derivative of #f(x)= sqrt(5+x^6)/x#?

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