Second Derivative and Graph-Need help with this problem

[stacytracey]

Find the interval where f(x) is increasing, the interval where f(x) is decreasing, and the local extrema:

f(x)=x^4+2x^3+5

So far I have this:
f'(x)=4x^3+6x^2=0
2x^2(2x+3)=0
x=0, -3/2

f"(x)=12x^2+12x=0
12x(x+1)=0
x=0, -1

I just dont know how to where f(x) is increasing, and decreasing, and the local extrema.

 

[skeeter]

what is the purpose behind finding critical values of f(x) ?

what does the 1st derivative test tell you?

what does the 2nd derivative test tell you?

these concepts are stated in your text ... look them up and see what they say.

 

[galactus]

Have you graphed your function to see what it looks like?. Always helps with these problems

 

[stacytracey]

Thank you Galactus. Let me try that and I will reply back.