For positive a, consider the family of functions y = arctan x + a 1 ax , x> 0. (a) Graph
Chapter 0, Problem 103(choose chapter or problem)
For positive a, consider the family of functions y = arctan x + a 1 ax , x> 0. (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. [Hint: Use the fact that ax = a x for a > 0, x > 0.]
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