Concavity help

[Tclements3]

Determine where the following function is concave up:

3x^5-5x^4-120x^3-430x+1

I know that the first derivitave is 15x^4-20x^3-360x^2-430
and the second derivitave is 60x^3-60x^2-720x = 60x(x^2-x-12) = 60x(x+3)(x-4)

That's where I get stuck. The answer key says it is concave up in [-2,0]U[3,inf) but I cannot figure out how to get there. Any help is appreciated!

 

[pka]

Determine where the following function is concave up:
3x^5-5x^4-120x^3-430x+1
I know that the first derivitave is 15x^4-20x^3-360x^2-430
and the second derivitave is 60x^3-60x^2-720x = 60x(x^2-x-12) = 60x(x+3)(x-4) That's where I get stuck. The answer key says it is concave up in [-2,0]U[3,inf) but I cannot figure out how to get there. Any help is appreciated!

Solve the following: 60x(x+3)(x-4)>0.

 

[Tclements3]

Solve the following: 60x(x+3)(x-4)>0.

It seems to me that 60x(x+3)(x-4)>0 at (-3,0)U(4,inf) but that doesn't match the answer on the key. Therein lies my problem.

 

[pka]

It seems to me that 60x(x+3)(x-4)>0 at (-3,0)U(4,inf) but that doesn't match the answer on the key. Therein lies my problem.

The answer key is wrong.

 

[Tclements3]

The answer key is wrong.

Ok, thanks! I was afraid it might be. My teacher has a habit of getting a couple of answers wrong on the key to his test reviews. It's incredibly frustrating because it causes me to spend hours banging my head against the wall trying to figure out why I'm getting the wrong answer on things that I thought I understood instead of using that time to get better at the stuff I do actually need to work on.