# How do you find the point of inflection of a cubic function?

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To find the point of inflection of a cubic function, follow these steps:

- Determine the second derivative of the cubic function.
- Set the second derivative equal to zero and solve for the value(s) of x.
- Plug the values of x obtained in step 2 into the original cubic function to find the corresponding y-coordinate(s).
- The point(s) (x, y) obtained in step 3 represent the point(s) of inflection of the cubic function.

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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.

- How do you find all points of inflection of the function #f(x)=x^3-3x^2-x+7#?
- How do you find points of inflection of #(1-x^2)/x^3#?
- For what values of x is #f(x)= (5x-x^3)/(2-x)# concave or convex?
- What are the points of inflection of #f(x)=x+sinx # on the interval #x in [0,2pi]#?
- Is #f(x)=(x-2)^3-x^4+x# concave or convex at #x=0#?

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