Originally Posted by

**oceanmd** Please help with the graph analysis

f(x)=x^3-3x^2+3

1.First derivative 3x^2-6x

2. intervals where f is increasing. 3x^2-6x=0, x=0, x=2 Function is increasing from -infinity to 0 and from 2 to infinity

3. decreasing (0,2)

4. local max point (0,3)

5. local min point (2,-1)

6. second derivative 6x-6

I hope everything until now is correct

7. inflection point 6x-6=0, x=1 Is it correct to say that at x=1 function changes from concave down to concave up?

8. what are the intervals where function is concave up and concave down?

Thank you very much