Question

How do you find the critical points on a graph?

Answer 1

In the given question, we have been given that there may be any graph $g$. We have to find the critical points on the graph. To do that, we need to know the meaning of ‘critical point’ on a graph. Then, we just need to write the basic, general points for finding the critical points on a graph.

Formula Used:
To find the critical points, we put the derivative of the given function equal to zero, i.e.,
$f'\left( x \right) = 0$

Complete step by step answer:
We are going to consider two cases:
Case One:
When we have been given a simple graph (no function given).
Then, in this case, all the points where the line is parallel to the x-axis and all the points where the line does not exist, are critical points.
Case Two:
When we have been given a function.
Then, in this case, we calculate the critical points by putting the value of derivative of the function $\left[ {f\left( x \right)} \right]$ equal to zero, i.e.,
$f'\left( x \right) = 0$

Note: In the given question, we were asked how we can find the critical points on a graph. We learned that if we have been given a simple graph (no function is given), then the critical points are all those points where the line is horizontal, or where the line does not exist. Then, if we have been given a function, then the critical points are calculated by putting the derivative of the function equal to zero. So, it is really important that we know the formulae and where, when, and how to use them so that we can get the correct result.