What is the extreme point of the curve 3x-6x^2?

We have to find the extreme point of the curve y = 3x -
6x^2.

To do that we find the first derivative of 3x - 6x^2
and equate it to zero. This is solved for x.

Now y = 3x -
6x^2

y' = 3 - 12x

3 - 12x =
0

=> 12x = 3

=>
x = 1/4

At x = 1/4, y = 3*(1/4) -
6*(1/4)^2

=> 3/4 -
6/16

=> 3/4
-3/8

=> 3/8

Also at x =
1/4, y'' is -12 which is negative. So we have the point of maxima at x =
1/4

The extreme point is at x =
1/4 and this is the maximum point with the
expression equal to 3/8.