For concavity, why second derivative of curve equals zero for all stationary points?
The second derivative does not equal zero for all stationary points. The second derivative equals zero at all points of inflection, which is what Scythian explained. At all stationary points, the first derivative equals zero. If the second derivative is positive, then the stationary point is a minimum turning point; if negative, then maximum. At all points, the second derivative indicates concavity: positive indicates concave upwards [Scythian’s driver, if following the curve from negative x values towards positive, has the steering wheel turned towards the left], negative is concave downwards [steering right], zero is where the concavity changes from up to down, or down to up [steering wheel is momentarily straight ahead while changing over from left turn to right, or from right turn to left], and that’s called a point of inflection. EDIT: That’s not quite correct about zero second derivative. The converse is true, at a point of inflection the second derivative is zero, but a zero sec
