What is the minimum values of the function v(x) = 3x^2 -3x +5 ?

Given the function:

v(x) =
3x^2 - 3x + 5

We need to find the minimum values of
v(x).

First we will determine the first derivative
v'(x).

==> v'(x) = 6x
-3

Now we will calculate the derivatives
zero.

==> 6x -3 = 0 ==> 6x = 3 ==> x =
1/2

Then, the critical value for v(x) is the point x =
1/2

Now we will find the values of
v(1/2).

==> v(1/2) = 3(1/2)^2 - 3(1/2)
+5

                   = 3/4 - 3/2 + 5 = (3 - 6 + 20)/4 =
17/4

==> The minimum value of the
function v(x) is the point (1/2, 17/4)