Graphing a fnct

[q_fruit]

Where is the function increasing or decreasing?

f(x) = 2x^3 - 3x^2 - 12x +5

I found the 1st derivative and then factored it out..

f^`(x) = 6x^2 - 6x - 12
= 6(x-2)(x+1)

So when (x-2)(x+1) > 0, it's increasing.

Why then, does the answer key say that it's increasing when x < -1 or x > 2? Shouldn't it be x > -1? If it were smaller than -1, it would turn the fnct into a negative number, no?

thank you.

 

[tkhunny]

(x-2)(x+1) > 0

When multiplying things, and hoping to get something greater than zero, those things must have the same sign, no?

Both Positive
Where is it that x-2>0 AND x+1>0?

Both Negative
Where is it that x-2<0 AND x+1<0?

 

[q_fruit]

Yes I agree...
So the answer should say x > -1 and x > 2 ?

 

[Gene]

It is a cubic so it goes either
up,down,up or
down,up,down.
It changes direction at x=-1 and x=2
x=0 is in the middle of that range.
When x=0 the slope is -2*1 so it is going down.
That means it is
going up till x=-1 then goes down till x=2 then
goes up forever.
It is decreasing when -1<x<2
It is increasing everywhere else.
If x=-5 it is (-5-2)(-5+1) which is positive.

 

[tkhunny]

So the answer should say x > -1 and x > 2 ?

Does x = 0 fit BOTH restrictions? The intersection is the solution for this piece.

What's the solution for the other piece?