Graph several curves in the family and describe how the

Question

Question: For positive a, consider the family of functions

y = arctan (√x + √a), x > 0
               (1 - √ax)

(a) Graph several curves in the family and describe how the graph changes as a varies.

(b) Use a computer algebra system to find dy/dx, and graph the derivative for several values of a. What do you notice?

(c) Do your observations in part (b) agree with the answer to part (a)? Explain.