Find the minimum value of the function f

Find the minimum value of the function f defined by f(x)=x^2-12x+9

diff(x^2 - 12*x + 9, x) = 2*x - 12

solve(2*x - 12 = 0)

x = 6

f(x):=(x^2 - 12 x + 9)

f(6) = 36 - 72 + 9

f(6) = - 27

Point(6; - 27) = minimum

If you want to see it:

Download Graph 4.4 from www.padowan.dk for free.

On "Axes", change the range of edge X from - 10 to 20, then "OK"

On "Axes", change the range of edge Y from - 30 to 20, then "OK".

On "Function I Insert function", type x^2 - 12*x + 9, then "OK".

The derivative f'(x)= 2x-12; set this equal to 0 and solve to get x=6; f(6)=-27.
the second derivative is 2 >0, so this is a minimum. Min of f is -27.

Hint:
By completing the square, you get:
f(x) = (x-6)^2 - 27
This should be enough for you to provide the answer.