If you had any kind of math skepticism as calculus student in high school or freshman year (or maybe you currently are), you may have wondered why we calculate areas under curves using integrals. Why the hell is area the opposite of differentiation? The relationship does not seem any intuitive. […]

## Math with LUF

“A good answer must be reinvented many times, from scratch.”

## If the derivative is positive, then the function is increasing

We all know Rolle’s theorem. It says that if is continuous on , differentiable on and satisfies , then there must be a such that . Few of us, though, know the proof of Rolle’s theorem. Unfortunately, it is given without proof in high school, and it is usually not […]

## LUF.def.1

Hello and welcome to this fresh forum, where we shall lively discuss, and develop, our mathematical knowledge. Lively we say, and fresh, and so we intend it to be, right in the middle of a dying, if not already dead, world. Not that we are expected to change the lot […]