-9x
1. We find the x intercepts by factoring out the x and putting into the quadratic formula. (-1.8,0), (0,0), (4.9,0)
2. Note that the y intercept is also (0,0).
3. The domain is R since this is a polynomial.
4. The function is continuous since it is a polynomial.
5. There are no vertical asymptotes since we have a polynomial.
6. The function is differentiable everywhere.
7. We find f (x) = 3x2 - 6x - 9 = 3(x - 3)(x + 1). We see that f is increasing on (- ,-1) and on (3, ). f is decreasing on (-1,3)
8. By the first derivative test, f has a relative maximum at (-1,5) and a relative minimum at (3,-27).
9. f (x) = 6x - 6 so that f is concave down on (- ,1) and concave up on (1, ).
10. f(x) has an inflection point at (1,-11).
11. f has no horizontal asymptotes.