How do you find all points of inflection for this function: #y = 4 / (9 + x^2)#?

Answer 1

Christopher Allers

You must study the second derivative of your function to get:

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Answer 2

Cameron Alexander

To find the points of inflection for the function $y = \frac{4}{9 + x^2}$ , you need to find where the second derivative $y''$ changes sign. First, find the first and second derivatives of $y$ with respect to $x$ . Then, set the second derivative equal to zero and solve for $x$ . The $x$ -coordinates obtained are potential points of inflection. Finally, check the concavity of the function around these points using the second derivative test to confirm if they are points of inflection.

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Answer from HIX Tutor

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.