relative maximum
When f ‘(x) changes fro positive to negative, f(x) has a
A relative maximum is a point on a graph where the function has the highest value in a localized region of the graph. This means that there may be other points on the graph where the function has a higher value, but they are outside of the region immediately surrounding the relative maximum point.
To find relative maxima, we need to examine the behavior of the function in a small neighborhood around each point on the graph. Specifically, we need to look at the sign of the derivative of the function.
If the derivative is positive to the left of the point and negative to the right of the point, then the point is a relative maximum. If the derivative is negative to the left of the point and positive to the right of the point, then the point is a relative minimum. If the derivative does not change sign at the point, then the point is a point of inflection.
Once we have identified a point as a relative maximum, we can find its coordinates by examining the values of the function at nearby points. The relative maximum will be the highest point in the region, and the coordinates of this point will give us the x and y values of the maximum.
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