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.
We’ll help your grades soar
Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.
- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support
Already a member? Log in here.
Are you a teacher? Sign up now