Question

What is a stationary point in Minima and Maxima?

Answer 1

Hint: This is a subjective question from differentiation and its various other components involved in it. The concept asked here is of stationary points and minima and maxima. First the analysis of first order differentiation is required and then the second order differentiation is required.

Complete step-by-step answer:
A stationary point of a function is defined as the point where the derivative of a function is equal to zero. This point is also referred to as the critical point and is used in the analysis of the behaviour of the function.
Mathematically, the above statement can be represented as
\[\dfrac{{dy}}{{dx}} = 0\]
To determine whether the stationary point is maxima or minima, the second derivative of the function is determined. Now, after calculating the second order derivative observe the sign of the function at the different stationary or critical points calculated above.
Now, if the second order differentiation gives a negative sign at the critical point or stationary point then that particular point gives a maxima, while if the sign of the second order differentiation at the critical point or stationary point then that particular point gives a minima.
Mathematically, the above statement can be represented as
\[\dfrac{{{d^2}y}}{{d{x^2}}} < 0\], the point gives a maxima
\[\dfrac{{{d^2}y}}{{d{x^2}}} > 0\], the point gives a minima

Note: This is a subjective question from the topic differentiation and concepts related to it. One, should be well versed with these topics to solve this particular question. Do not overthink about these concepts. You should learn the analysis of function using these concepts to make the theory crystal clear.