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

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

By signing up, you agree to our Terms of Service and Privacy Policy

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.

By signing up, you agree to our Terms of Service and Privacy Policy

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.

- For what values of x is #f(x)=-x^2+e^x# concave or convex?
- How do you determine the intervals where #f(x)=x^(2/3)+3# is concave up or down?
- If #y = x^2 ln x#, what are the points of inflection, concavity and critical points?
- How do you find the first and second derivative of #(lnx)^2#?
- If #f '(x) = 8x^3 - 16x#, how do you use the second derivative test to find maximum and minimum?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7