Local maximum

Definition

A local maximum of a function is a point at which the function's value is higher than at any nearby points. It represents a peak within a specific interval.

5 Must Know Facts For Your Next Test

1. A local maximum occurs where the first derivative of the function changes from positive to negative.
2. If $f'(c) = 0$ and $f''(c) < 0$, then $f(c)$ is a local maximum.
3. Local maxima are found using critical points, where the first derivative is zero or undefined.
4. The second derivative test can help determine if a critical point is a local maximum.
5. Local maxima are not necessarily the highest points on the entire graph, only within their immediate vicinity.

Review Questions

Related terms

Critical Point: A point on the graph where the first derivative is zero or undefined.

Global Maximum: The highest point over the entire domain of a function.

Second Derivative Test: A method used to determine if a critical point is a local minimum, local maximum, or neither by evaluating the second derivative at that point.