y' is increasing

Question

The values of x for which y= 2x³ - 12x² +18x +7=0 is increasing are?

Answer 1

Hello Tiarne,

 

To find where this function is increasing, we have to find where the derivative in negative.

y= 2x³ - 12x² +18x +7

y'=6x²-24x+18

 

We need to find the x intercepts, so set equal to 0.

0=6x²-24x+18

0=6(x²-4x+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