Relative minimum

[Vader07]

Find the input value that yields the relative minimum of the function

f(x) = 4x^3 -6x^2 - 12x + 5


This is what i did so far
12x^2 - 12x + 12

which lead to x^2 - x + 1
this gave me a quadratic equation to solve it but when I tried to solve it, it did not work out

any ideas or tips would be greatly appreciated

 

[wjm11]

Find the input value that yields the relative minimum of the function

f(x) = 4x^3 -6x^2 - 12x + 5


This is what i did so far
12x^2 - 12x + 12

which lead to x^2 - x + 1
this gave me a quadratic equation to solve it but when I tried to solve it, it did not work out

You just have a sign error. f'(x) = 12x^2 - 12x + 12 should be

f'(x) = 12x^2 - 12x - 12, then

0 = x^2 - x -1

rel. min. at x = (1 + 5^.5)/2