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