The values of x for which y= 2x

^{3}- 12x^{2}+18x +7=0 is increasing are?-
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The values of x for which y= 2x^{3} - 12x^{2} +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= 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

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