Given the function: h(x) = 5x-3x^2

We need to find the extreme values for h(x)

First, we need to find the first derivative h'(x).

==> h'(x) = 5 - 6x

Now we will determine the derivatives zero.

==> 5 - 6x = 0

==> x = 5/6

Then, the function h(x) has an extreme values when x = 5/6

==> h(5/6) = 5(5/6) - 3(5/6)^2

= 25/6 - 3(25/36

= 25/6 - 75/36 = 75/36 = 25/12

==> h(5/6) = 25/12

We also notice that the sign of x^2 is negative.

**Then, the function has maximum values at the point ( 5/6, 25/12)**

**Or at h(5/6) = 25/12**

## 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