Answer the following questions for the function f(x) = - 8x3 - 24x2 + 192x - 10. a. Find formulas for f'(x) and f"(x). f'(x)= D f"(x)= D Enter f(x), f'(x), and f"(x) into your grapher to examine the table. b. The formula for the first derivative f'(x) can be factored. Set f'(x) = 0 to find the two critical numbers. Hint: You can factor out - 24 from all terms in the formula for f'(x). You can also scroll the table function on your calculator. The critical values are x = D. (Use a comma to separate answers as needed.) c. Use your table to complete the following. At the negative critical value listed in part b, what does your table tell you about the value of the second derivative? f" (CD = E (Type integers or simplified fractions.) Consequently, what can be concluded about the graph of 1'? Select the correct choice below and, if necessary, fill in the answer boxes within your choice. ":3 A. The graph off is concave up and f has a relative maximum at( , ). -":;. B. The graph off is concave down and fhas a relative maximum at ( , ). 5:} c_ The graph off is concave up and f has a relative minimum at ( , ). (f; D. The graph off is concave down and fhas a relative minimum at( , ). "j; E. No conclusion can be made. d. Use your table to complete the following. At the positive critical value listed in part b, what does your table tell you about the value of the second derivative? f" (D) = Cl (Type integers or simplified fractions.) Consequently, what can be concluded about the graph of f? Select the correct choice below and, if necessary, fill in the answer boxes within your choice. (:3, A. The graph off is concave up and f has a relative minimum at ( , ). ('13. B. The graph off is concave down and fhas a relative maximum at ( , ). 5:} c_ The graph off is concave up and f has a relative maximum at( , ). D. The graph off is concave down and fhas a relative minimum at( , ). 9. Set the formula for the second derivative f"(x) = O to find any possible inection points. Hint: Atable on a grapher may or may not show when f"(x) = 0 depending on what your step size is, so use the formula or adjust your step size. f"(x)=0 at X: What can be concluded about the graph offat this value of x? Select the correct choice below and, if necessary, ll in the answer boxes within your choice. '11:} A- There is a point of inection at ( , ) where the graph of 1' changes from concave down to concave up. {:9 3- There is a point of inection at ( , ) where the graph of f changes from concave up to concave down. {:1- C. No conclusion can be made. f. Choose the graph ofthe function f(x). iii:- A. {:1} B. {12- c. {i} D. y Y y 800 9' 800 9' 00 9' X x Q\ x 0' i 5 15 0\ >15 15 D) >30 30 D)- D) 00 >4 0 >800