# What are horizontal points of inflection?

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Horizontal points of inflection are points on a curve where the concavity changes from concave upward to concave downward, or vice versa. At these points, the second derivative of the function is zero, but the function itself may not have a local maximum or minimum.

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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 of #f(x)=8x^2sin(2x-pi) # on # x in [0, 2pi]#?
- How do you sketch the graph of #f(θ)=2cosθ+cos2 θ# for #0≤x≤ 2π# using the first and second derivative?
- What is the first derivative test to determine local extrema?
- What are the points of inflection, if any, of #f(x)=x^4/(x^3+6 #?
- How do you find the maximum, minimum and inflection points and concavity for the function #y=1/5(x^4-4x^3)#?

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