Question

Where can local extrema occur?

1) At critical points
2) At endpoints of the domain
3) At points where the derivative is undefined
4) All of the above

Answer 1

Local extrema can occur at critical points, at endpoints of the domain, and at points where the derivative is undefined. Hence, they can occur in all the situations listed in the options provided.

Step-by-step explanation:

Local extrema in a function, which are the highest or lowest points in a certain interval, can occur in different situations. They can occur:

1. At critical points, where the derivative of the function is zero.
2. At endpoints of the domain, especially if the domain is limited or the function is defined on a closed interval.
3. At points where the derivative is undefined, which might be due to a cusp or vertical tangent in the function.

Therefore, the correct answer is 4) All of the above.