Calculate the exrtreme value of the function f(x) = 3x^2-4x+5

f(x)= 3x^2 - 4x + 5

we need
to find the extreme value of f(x).

First we will find the
critical points.

==. f'(x) = 6x -4 =
0

==> x = 4/6 =
2/3

Then the function f(x) has an extreme value at
f(2/3)

==> f(2/3) = 3*(2/3)^2 - 4*2/3 +
5

==> f(2/3) = 12/9 - 8/3 + 5 = ( 12 - 24 + 45) / 9
= 33/9 = 11/3

Then the function has extreme
value at the point f(2/3) = 11/3 OR the point ( 2/3, 11/3)