How Do You Analyze the Function f(x) = ax + (b/x) for Extrema and Concavity?

[tachu101]

Homework Statement

4) Let f(x)= ax+(b/x) where a and b are positive constants.
(a) Find in terms of a and b, the intervals on which f is increasing.
(b) Find the coordinates of all local maximum and minimum points.
(c) On what interval(s) is the graph concave up?
(d) Find any inflection points. Explain your answer.

The Attempt at a Solution

I need to take the derivative so it is f'(x)= a-b(x^-2) then I set this equal to zero to find the critical points, but then I'm not sure what value to solve for. X? If I do that I get critical points at +/- $$\sqrt{}b/a$$

 

[HallsofIvy]

If you set a- bx^-1 equal to 0, the only thing left to solve for is x! Yes, $x= \sqrt{b/a}$ and $x= -\sqrt{b/a}$ are the critical values of x. What does that tell you about a, b, c, and d?

 

[tachu101]

so is the function increasing from (-infinity,-root(b/a)) union (root(b/a),infinity)? Then should I take the second derivative set it equal to zero to find the inflection point