Question: Consider the family of functions
f(x) = (√(a + x)/(√a + √x)), x ≥0, for positive a.
(a) Using a computer algebra system, find the local maxima and minima of f.
(b) On one set of axes, graph this function for several values of a. How does varying a affect the shape of the graph? Explain your answer in terms of the answer to part (a).
(c) Use your computer algebra system to find the inflection points of f when a = 2.