Haocheng Z. answered • 03/21/21

Professional Tutor, NCEES Certified EIT, Mechanical Engineer

Whenever the derivative(slope) of a curve is equal to zero, we can call that point a potential minimum or potential maximum which also indicates a potential concave up or concave down.

In this case, concave up occurs at pi*n < x < pi/2 +pi*n.

Concave down occurs at pi/2 +pi*n < x < pi*n.

When the 2nd derivative of a function is the equation to 0 at a certain point, we can call that point a point of inflection. In this case, point of inflection occurs at pi*n where n are integers such as 0, 1, 2, etc.