I am stuck on this problem, and I am thinking that I am not getting the derivatives (1st and 2nd) correct. Here is the problem:
F(X)= 2X(X+4)^3
I know I have to get the first and second deriviative's but don't I need to cube the inside function first and then distribute the 2x to it? Or does the power rule come into effect here? I have tried cubbing the inside terms and then distributing the 2x but it doesn't seem to give me the correct zeros's of the graph so if someone could illustrate. Please Help, Thanks.
I'm sorry for the first derivative how are you getting the 6X? Is this the power rule being used within the product rule?
How would I determine where the function is increasing and decreasing, where its concave up and down and the inflection points. I know you have to know the zero's of the derivative(s).
So are you saying it would be easier to use the product rule? I still don't see where the 6X(X+4)^2 comes from, but how would I determine my zero's from here which will result in the x points on the graph?
My book says the function is increasing for x> -1 decreasing for x< -1 concave upward for x<-4 and x> -2 concave downward at -4< x < -2 minimum at (-1) and inflection at (-4,0) and (-2,-32)
Could someone show how I find these?
I've just re-read my reply and it's pretty plain what I said: "Personally ... I'd expand f(x) first ... I think that's the easier road to hoe."
I cannot see how you could possibly think I said it would be easier to use the product rule.
On the topic of the product rule, do you understand how it works in this question? In particular, do you understand that the second term is 2x times 3(x + 4)^2? Is it becoming clearer now where the 6X(X+4)^2 comes from?
Edit: Your potential x-coordinates for the stationary points will come form solving a quadratic equation. I assume solving a quadratic is money for jam for you ....