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y' is increasing

The values of x for which y= 2x3 - 12x2 +18x +7=0 is increasing are?
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Hello Tiarne,
To find where this function is increasing, we have to find where the derivative in negative.
y= 2x3 - 12x2 +18x +7
We need to find the x intercepts, so set equal to 0.
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: