Question

How do you find the stationary points of a function?

Answer 1

Hint : First we will specify the stationary points and their rules. After that we will consider a function for explanation. Then using that function we will explain the stationary points and how to evaluate them. Also, define what are turning points.

Complete step-by-step answer :
We will start by defining the stationary point of a function. So, a stationary point of a function suppose $f(x)$ is a point where the derivative of $f(x)$ is equal to zero. These points are called stationary points because at these points the function is neither increasing nor decreasing. Also, when we see the graphs these points correspond to points on the graph of $f(x)$ where the tangent to our curve is a horizontal line.
In order to evaluate the stationary points of a function that we have considered earlier $y = f(x)$. So, here the stationary points will be given by,
$\dfrac{{dy}}{{dx}} = 0$
This repeats in mathematical notation the definition given which we have mentioned above, which stated that the points where the gradient or the slope of the function becomes zero.
Also, a stationary point is called a turning point if the derivative changes its sign at that point.

Note : Remember and practice all the values of the derivatives while solving such type of questions. Make sure when deriving any expression always back trace to see if you have solved correctly. Also, remember that all turning points are stationary points, but not all the stationary points are turning points.