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**.

## See eNotes Ad-Free

Start your **48-hour free trial** to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Already a member? Log in here.