Question

What is stationary point in maxima and minima?

Answer 1

Stationary points:

1. This question arising from differentiation and its several other components. The notion being asked for here is that of stationary points, minima, and maxima. The analysis of first order differentiation is necessary initially, followed by the analysis of second order differentiation.
2. A function's stationary point is defined as the point at which its derivative equals zero. This point, also known as the critical point, is employed in the analysis of the function's behaviour.
3. The preceding sentence can be represented mathematically as $\frac{dy}{dx}=0$.
4. The second derivative of the function is used to determine whether the stationary point is maximum or minima. Now, after calculating the second order derivative, look at the sign of the function at each of the previously obtained stationary or crucial locations.
5. Now, if the second order differentiation has a negative sign at the critical point or stationary point, that point produces a maxima, whereas if the second order differentiation has a positive sign at the critical point or stationary point, that point gives a minima.
6. The preceding statement can be represented mathematically as $\frac{d^{2}y}{d{x}^2}<0$, the point gives a maxima
   $\frac{d^{2}y}{d{x}^2}>0$, the point gives a minima