inflection point, concave up and down question
Please help with the graph analysis
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
when the second derivative is a positive number
Please explain if I am wrong. Thank you very very much.
F(x) = 3x^2 + 12x + 3
Please correct me if I am wrong
1. We need to find first derivative to find minimum and maximum points
First derivative = 6x +12, 6x + 12 = 0, x = -2
2.Local minimum is (-2, -9)
3. Second derivative = 6 What does it mean? Where is the inflection point? There is no inflection point. Right? Is it correct to say that because the second derivative is a positive number, the graph is always concave up. For this particular function the graph is concave up from negative infinity to positive infinity.