Hi

Is a terraces-or. Saddle point actually a hybrid of turning point because slope changes from 0 to a positive or negative value, and local maximimum as slope = 0, and it follows that a terrace point / saddle point really but in any derivation the value should be 0 or not and thus would not have f '' 'is not equal to 0 but f' '' = 0 for a terraces-saddle point, right? What I understand wrong?

thx

## The best answer

A deck / saddle point is a *special* turning point, namely one with a horizontal tangent. An extreme point, it is not so.

This is similar: a square is a special rectangle, a car is a special type car ...

a saddle point is a turning point with horizontal tangent;

Therefore f "= 0 **and** f '= 0