What is the minimum point of f(x)=4x^2 -4x +5

Given the curve:

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

We need to find the minimum value of the curve
f(x).

First we know that the coefficient of x^2 is
positive. Then, f(x) has a minimum value.

Now we will
determine the first derivative zeros.

==> f'(x) = 8x
-4 = 0

==> 8x =
4

==> x = 1/2

Then the
function has a minimum when x= 1/2

==> f(1/2) =
4(1/2)^2 -4(1/2) + 5

                 = 4*1/4 - 2 + 5 = 1
-2 + 5 = 4

Then the curve f(x) has a minimum
value f(1/2) = 4 or the point ( 0.5, 4)