Stationary Point:
A stationary point in calculus is a point on the graph of a function where the derivative is equal to zero or is undefined.

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In other words, at a stationary point, the rate of change of the function is either zero or undefined. Stationary points include local minima, local maxima, and points of inflection.

Inflexion Point:
An inflection point is a point on the graph of a function where the curvature changes sign. At an inflection point, the second derivative of the function is equal to zero or undefined. The graph transitions from being concave upward to concave downward or vice versa.

Relationship between Stationary Point and Inflexion Point:
Not all stationary points are points of inflection. While every inflection point is a stationary point, a stationary point may or may not be an inflection point. The distinction lies in the behavior of the curvature.

Stationary Point Not at an Inflexion Point:
If the curvature remains the same on both sides of the stationary point (e.g., concave upward on both sides), it is not an inflection point.
Diagram: f(x) | /\ | / \ | / \ | / \ Stationary point, not an inflection point |/ \ |__________\ x
Stationary Point at an Inflexion Point:
If the curvature changes sign (e.g., concave upward on one side and concave downward on the other), it is an inflection point.
Diagram:
f(x) | /\ | / \ | / \ | / \ Stationary point and inflection point |/ \ |__________\ x

In summary, a stationary point is a broader concept that includes points of inflection, but not all stationary points exhibit the curvature change characteristic of inflection points.