Understanding Relative Maximum in Calculus | Definition, Examples, and Differences from Absolute Maximum

Relative max

In calculus, a relative maximum, also known as a local maximum, is a point on a graph where the function reaches its highest value within a specific interval or region

In calculus, a relative maximum, also known as a local maximum, is a point on a graph where the function reaches its highest value within a specific interval or region.

To determine if a point is a relative maximum, we must first find the critical points of the function. Critical points occur where the derivative of the function is either zero or does not exist. Once we have identified the critical points, we can examine the values of the function at these points as well as the values of the function at the boundary points of the interval of interest.

If the value of the function at a critical point is higher than the values of the function at neighboring points, then that critical point is a relative maximum. However, it is essential to note that a relative maximum does not necessarily indicate that the function has the highest value over its entire domain. It is just a local high point within a specific interval.

To visualize a relative maximum on a graph, you can imagine a curve that reaches a peak and then starts to descend. The point at the peak is the relative maximum.

It’s important to distinguish between relative maximum and absolute maximum. An absolute maximum refers to the highest point on the entire graph of the function, while a relative maximum refers to the highest point within a specific interval or region.

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