For what value(s) of x does 4x^6 - 8x^3 + 18 have a relative minimum?
Hello,
Let X be x^3, then you can go back to a polynomial of second degree, which you can derivate easily and find the value that annulates it.
->4X^2-8X+18
Derivative : 8X-8
Annulates in X=1 (negative then positive -> the initial function decreases first then increases -> it's a minimum)
<=> x^3=1
<=> x=1