continuous function

The Weierstrass theorem states that a continuous function defined on a closed and bounded interval attains both its minimum value and its maximum value at some points of that interval.

The Intermediate Value Theorem states that if a function is continuous on a closed interval, then it takes every value between its values at the endpoints.

A function is continuous if the limit at each point exists and coincides with the function’s value, ensuring no abrupt changes in its behavior.

The Mean Value Theorem for Integrals states that a continuous function attains its average value at least once over a closed interval.