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

*print*Print*list*Cite

### 1 Answer

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)**