Raynal's Theorem

Raynal's Theorem relates to the behavior of continuous functions. It states that if a function is continuous on an interval and has the same value at two different points within that interval, then there must be at least one point between them where the function's slope (or derivative) is zero. In simple terms, if you plot the function and look at two points with the same height, somewhere in between, the function must level off or have a flat spot. This theorem helps us understand that functions can't just jump around without moments of zero slope when they start and end at the same value.