Question

What is the relative maximum and minimum of the function?

Answer 1

We are asked in the question to explain about the relative maximum and the relative minimum of the function. A relative maximum is a peak in the graph whereas a relative minimum is a bottom in the graph. The function is evaluated for its crests and troughs for its relative minimum and maximum.

Complete step by step solution:
According to the given question, we are asked in the question to explain about the relative maximum and the relative minimum of the function.
Relative maximum refers to a point where the function changes its direction from increasing to decreasing. They are generally observed as ‘peaks’ in the graph.
Relative minimum refers to a point where the function changes its direction from decreasing to increasing. They are generally observed as ‘bottom’ in the graph.
For example – we have a graph as shown below.

Here, the points A and C are the relative maximum of the function as they have peaks which are changing direction from increasing to decreasing.
The point B is the point of relative minimum as can be seen as the bottom of the function and also the direction change from decreasing to increasing.

Note: Absolute maximum is a point of the greatest possible that a given function can obtain. Similarly, absolute minimum is a point of the least value that a given function can obtain. The relative maximum and the relative minimum for a function can be found using the first derivative test which makes use of the critical values.