What does stationary point mean in a curve? And what does nature of the stationary point mean?

Answer 1

Stationary points of a curve are its critical points. More specifically, using the FIRST derivative of the curve, stationary points (critical points) are the points on the graph where the f'(x) = 0 or f'(x) = undef. When f'(x) = 0, that point can be a relative maximum, a relative minimum, or even a point of inflection. When f'(x) = undef. (including infinity and negative infinity), that point is not actually a point but a large discontinuity where either side of that point approaches infinity or negative infinity values.

The nature of a stationary point is simply if the graph at that point is concave up, concave down, or neither. It is determined using the SECOND derivative of the curve f"(x). If f"(x) > 0, the curve at that point is concave up (tends to look like a U), meaning that the point is a relative minimum. Likewise, if f"(x) < 0, the curve at that point is concave down (tends to look like an upside-down U), meaning that the point is a relative maximum. But if f"(x) = 0, then that point is a point of inflection, meaning that the concavity of the curve on either side of that point is different.

Answer 2

What Does Stationary Mean

Answer 3

Stationary points are also known as critical points, i.e. Maximum, Minimum, and possibly points of inflection. They are defined by a function's derivative in that they will vanish in the set of dependent values after differentiation of the parent equation.