# What are the points of inflection, if any, of #f(x) =-3x^3 - 7x^2 + 3x#?

The point of inflection is

The first and second derivatives are computed.

When is the turning point?

As a result, the turning point is

We could create a chart.

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To find the points of inflection, we need to find where the second derivative changes sign. The second derivative of f(x) = -3x^3 - 7x^2 + 3x is f''(x) = -18x - 14. Setting f''(x) equal to zero gives us x = -7/18. This is the only critical point. To determine if it's a point of inflection, we need to check the concavity around it. Calculate the second derivative at a point greater than -7/18, for instance, x = 0, we get f''(0) = -14. This indicates the function is concave down to the left of x = -7/18. Similarly, calculating the second derivative at a point less than -7/18, for instance, x = -1, we get f''(-1) = 4. This indicates the function is concave up to the right of x = -7/18. Therefore, x = -7/18 is a point of inflection.

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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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