The derivative of y at a certain point is zero, so this point is called stagnation point, which may be an extreme point, such as:

Y = the square of x, or y = the cube of x, they are not necessarily extreme points.

And the second derivative of this point is not necessarily zero. Such as function

Square of Y =

The first derivative at X=0 is zero, but the second derivative is not zero.

Of course, if the derivative of a function is always zero, it will be too simple, as the upstairs said. I don't think the landlord meant that!