Determine the extreme value of the function h(x) = 5x-3x^2

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