# How do you find all points of inflection given #y=2x^2+4x+4#?

There are no points of inflection.

The second derivative is a constant value (4), meaning that the second derivative is defined always (it's 4), and it will never change sign. Thus, there are no points of inflection. This is demonstrated also by the graph, which is a "bowl up" parabola, and thus never changes from bring "bowl up" to "bowl down".

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To find the points of inflection for the function (y = 2x^2 + 4x + 4), follow these steps:

- Calculate the second derivative of the function.
- Set the second derivative equal to zero and solve for (x).
- Once you have the (x)-values where the second derivative equals zero, plug these values into the original function to find the corresponding (y)-values.

Let's go through these steps:

- The first derivative of (y = 2x^2 + 4x + 4) is (y' = 4x + 4).
- Taking the derivative of (y'), the second derivative is (y'' = 4).
- Setting (y'') equal to zero gives (4 = 0), which is not solvable because it's a constant.
- Since the second derivative is a constant, there are no points of inflection for the function (y = 2x^2 + 4x + 4).

In summary, the function (y = 2x^2 + 4x + 4) does not have any points of inflection because its second derivative is a constant, indicating no change in concavity.

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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.

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- How do you find the y coordinate of the inflection point of the function #f(x)= 10(x-5)^3+2#?

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