# How do you find the inflections points for #g(x) = 3x^4 − 6x^3 + 4#?

The graph's inflection points are the places where the concavity changes. To locate these points, we must first examine the concavity, which requires knowledge of the second derivative's sign.

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To find the inflection points for the function (g(x) = 3x^4 - 6x^3 + 4), follow these steps:

- Find the second derivative of the function, (g''(x)).
- Set (g''(x) = 0) and solve for (x) to find the points where the concavity changes.
- Determine the (x)-coordinates of the inflection points by solving for (x) in the equation (g''(x) = 0).
- Evaluate (g(x)) at each of these (x)-values to find the corresponding (y)-coordinates.

Let's find the second derivative of (g(x)):

[g(x) = 3x^4 - 6x^3 + 4]

[g'(x) = 12x^3 - 18x^2]

[g''(x) = 36x^2 - 36x]

Now, set (g''(x) = 0) and solve for (x):

[36x^2 - 36x = 0]

[36x(x - 1) = 0]

[x = 0 \quad \text{or} \quad x = 1]

So, the possible inflection points occur at (x = 0) and (x = 1).

Next, evaluate (g(x)) at these (x)-values to find the corresponding (y)-coordinates:

When (x = 0): [g(0) = 3(0)^4 - 6(0)^3 + 4 = 4]

When (x = 1): [g(1) = 3(1)^4 - 6(1)^3 + 4 = 1]

Therefore, the inflection points for (g(x) = 3x^4 - 6x^3 + 4) are (0, 4) and (1, 1).

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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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