The problem goes specifically like this:
If h is differentiable and has positive derivative that pass through (0,0), and is continuous and positive. If:
Find the intervals where f is decreasing and increasing, maxima and minima.
My try was this:
The derivative of f is given by the chain rule:
We need to analyze where is positive and negative. So I solved the inequalities:
That gives: for the first case and for the second one. Then (not sure of this part) and if Also if both h′ and are negative the product is positive, that's for .
The case of the product being negative implies:
So the function is increasing in . So the function does not have maximum or minimum. Not sure of this but what do you think?