At what value of the argument will the value of the function y = – x2 + 6x-4 be the largest?

The function takes its greatest value at the maximum point. A point is an extremum of a function if the derivative of the function is zero or does not exist in it.
Find the derivative y ‘= (- x2 + 6x-4)’ = – 2x + 6.
Let’s equate it to zero:
y ‘= 0;
-2x + 6 = 0;
2x = 6;
x = 6/2 = 3.
At the point x = 3, the function y = -x2 + 6x-4 has an extremum.
The function has a maximum at the points at which the second derivative takes negative values.
y ” = – 2.
The second derivative of this function is negative over the entire domain of definition, which means that the function is convex for any values ​​of x, and accordingly has no minima.
This means that the function y = -x2 + 6x-4 has a maximum at x = 3.