find the minimum of f(x) = 2x^2 - 4x + 3

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

First we
need to determine f'(x)

f'(x) = 4x -
4

Now we need to find the critical values for f(x) which is
f'(x)'s zero.

4x - 4 =
0

==> 4x = 4

==>
x= 1

Then f'(x) has a minimmum values at x=
1

==> f(1) = 2(1) - 4(1) +
3

              = 2 - 4 +
3

              = 1

Then f has
a minimmum value at (1, 1)