The Leibniz theorem states that a function that is continuous on the interval [a, b] and differentiable on the interval (a, b) has the same derivative as th...
The Leibniz theorem states that a function that is continuous on the interval [a, b] and differentiable on the interval (a, b) has the same derivative as the function evaluated at the midpoint of the interval, that is, the average of the function values at the endpoints of the interval.
In simpler terms, the theorem says that the derivative of a function on an interval is equal to the average rate of change of the function on that interval.
The proof of the Leibniz theorem relies on the definition of the derivative and the properties of continuous functions and differentiable functions.
One of the key applications of the Leibniz theorem is to differentiate functions that are continuous but not differentiable at a single point