Here is a problem that I'm really struggling with: f(x)=2-2x-x^3. F prime of this function is -2-3x^2 and when setting to zero to find critical numbers, you end up taking the sq. root of -2/3. So there are no critical numbers.

I'm supposed to determine concavity and find inflection points. Per the second derivative test rules, F prime c must equal 0 and f double prime must exist near c. Since F prime C doesn't equal zero, as there are no critical numbers, is the graph also not concave up/down and are there also no inflection points? Am I getting this right?

I'm so confused, Thank you.