Question

I just want to check my answer for:
Find all values of x such that f(x)<0 and f(x)>0, and sketch the graph of f when:

\[\f(x)=-\frac{1}{9}x^3-3\]

Answer 1

\[-\frac{1}{9}x^3-3>0\]
\[-\frac{1}{9}x^3>3\]
\[x^3<-27\]
\[x^3+27<0\]
\[(x+3)(x^2-3x+9)<0\]
So how do I know where f(x)>0? If it switched.

Answer 2

@zepp

Answer 3

In fact, you are asking to get all value of x where y is positive, and negative, right?

Answer 4

So you should try to find its root first, which is there:, then simply say, from minus infinity to this x value, the function is positive and from the x value to infinity, the function is negative.