The values of x for which y= 2x^{3} - 12x^{2} +18x +7=0 is increasing are?
Hello Tiarne,
To find where this function is increasing, we have to find where the derivative in negative.
y= 2x^{3} - 12x^{2} +18x +7
y'=6x^{2}-24x+18
We need to find the x intercepts, so set equal to 0.
0=6x^{2}-24x+18
0=6(x^{2}-4x+3)
0=6(x-3)(x-1)
x=3 or x=1
When y' is positive, this means that the original function has a positive slope and is increasing. Since y' is a parabola that opens upward, it is negative only for values between 1 and 3, and positive outside of these values.
So we can say that y is increasing at:
-∞<x<1 and 3<x<∞
and y is decreasing at:
1<x<3