T Consider the two-parameter family of functions of the form Mr) : {1(1 e 'bx]. where o. and b are positiv'e real numbers. a] Find the first derivative and the critical numbers of it. Use these to construct a first derivative sign chart and determine for which values of x the function h is increasing and decreasing. b] Find the second derivative and build a second derivative Sign chart. For which values of I. Is a function in this family concave up? Concave down? c) What is the value of Jim a(1 9"\")? Jim a(1 9'\")? (Hint: Lookat HWZ for what are Irm 1* |35 the limits of e I.) d] How does changing the value of it affect the Shape of the CUIVe? e] Sketch the graph of a typical member of this family. Write several sentences to desoribe the overall behavior of a typical function h and how this behavior depends on o and b