Locating critical points Find the critical points of the following functions. Assume a is a nonzero constant.


ƒ(x) = x² √(x + 5)

Verified step by step guidance

1. First, find the derivative of the function ƒ(x) = x² √(x + 5) using the product rule and the chain rule.
2. Set the derivative equal to zero to find the critical points, as critical points occur where the derivative is zero or undefined.
3. Solve the equation obtained from setting the derivative to zero for x to find potential critical points.
4. Check the domain of the original function to ensure that the critical points found are valid within the context of the function.
5. Evaluate the behavior of the function around the critical points to determine if they are local maxima, minima, or points of inflection.