Chapter 4.4, Problem 6E

In Exercises 1–6, investigate the one-parameter family of functions. Assume that a is positive.

1. (a) Graph f(x) using three different values for a.
2. (b) Using your graph in part (a), describe the critical points of f and how they appear to move as a increases.
3. (c) Find a formula for the x-coordinates of the critical point(s) of f in terms of a.

$f(x)=\frac{a}{x^2}+x\mathrm{for}x>0$