What means zero derivative for the function y=x^2-6x+3?

Zero derivative of a function means that the function has
a local extreme point, minimum or maximum, for a root of 1st derivative of the
function.

The root of derivative represents the critical
point of the function.

Usually, we'll determine zero
derivative when we want to find out the extreme points of the
function.

For instance, we want to determine the zero
derivative of the function:

y = x^2 - 6x +
3

dy/dx = 2x - 6

2x - 6 =
0

2x = 6

x =
3

So, x = 3 is the zero derivative and
it represents the critical point and f(3)=9 - 18 + 3 = -6 => f(3) = -6 represents
the minimum point of the function.