Page 6 > of 9 - ZOOM + 4. Consider the functions defined by p(x) = 23 - 12r. a. Find p'(r) and determine the critical numbers of p. How many critical numbers does p have? b. Construct a first derivative sign chart for p. What can you say about the overall behavior of p ?Page 7 of 9 - ZOOM + c. Find p"(x) and construct a second derivative sign chart for p. What does this tell you about the concavity of p ? [1] d. Without using a graphing utility, sketch and label typical graphs of p(x) . Label all inflection points and local extrema.Page 8 > of 9 - ZOOM + 5. Consider the functions of the form h(z) = 10 (1 - e-0.2r) a. Find the first derivative and the critical numbers of h. Use these to construct a first derivative sign chart and determine for which values of r the function h is increasing and decreasing. [1 b. Find the second derivative and build a second derivative sign chart. For which values of a is a function in this family concave up? concave down? [1] c. What is the value of lim, too 10 (1 - e-02r) ? lim, , . 10 (1 - e-0.2x) ? [1] d. Sketch the graphPage 9 of 9 - ZOOM + 6. For each family of functions that depends on one or more parameters, determine the function's absolute maximum and absolute minimum on the given interval. a. p(x) = 13 -ax, [0, a] (a > 0) c. w(x) = a(1 -e-bz), [b, 3b] (a,b > 0) [1]