Find the maximum or minimum value of f(x) = -3x^2 + 9x

Given the curve f(x) = -3x^2 +
9x.

We need to find the extreme value of the
function.

First we notice that the coefficient of x^2 is
negative, then the curve will have a maximum point.

Now we
will find the first derivative.

=> f'(x) = -6x +
9

Now we will determine the critical value which is the
derivatives zero.

==>< -6x + 9 =
0

==> x = -9/-6 = 9/6 =
3/2

==> x = 3/2

Now we
will calculate f(3/2)

==> f(3/2) = -3(3/2)^2 +
9(3/2) = -27/4 + 27/2 = 27/4

Then the
function f(x) has a maximum value at the point (3/2,
27/4)