What does the derivative $\displaystyle f'(x)$ for $\displaystyle x \in [0, \infty)$ say about $\displaystyle f(x)$ for $\displaystyle x \in [0, \infty)$?
What does the derivative $\displaystyle f'(x)$ for $\displaystyle x \in [0, \infty)$ say about $\displaystyle f(x)$ for $\displaystyle x \in [0, \infty)$?
so can I just say this:
f '(x) = nx^(n-1)
this is always positive for x>0 and n>1
I think because of the problem statement it is okay to say the function is increasing on the entire interval. You know it is differentiable, because the function and its derivative are continuous.
I think because of the problem statement it is okay to say the function is increasing on the entire interval. You know it is differentiable, because the function and its derivative are continuous.