The local maximum of the function f(x) is (0,64)
Given,
From the table we can notice that when ₋2<x<0, f(x) is increasing
And in case of when 0<x<3, f(x) is decreasing progressively.
we know that a local maximum is present on the graph of the function y=f(x) at the location where the graph shifts from increasing to decreasing. The tangent has zero slope at this location. And at the point when the graph shifts from declining to increasing, a local minimum is present.
Therefore, a local maximum also known as relative maximum, is a maximum that exists in a certain area and is not necessarily(but could be) a global maximum.
Hence f(0) is a local maximum of the ordered pair (0,64)
Hence we get the local maximum pair as (0,64)
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