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find the x values of all points where the function has any relative extrema http

ID: 2878302 • Letter: F

Question

find the x values of all points where the function has any relative extrema https://www.mathxi.com/Student/PlayerHomework.aspx?homeworkld 375140243&questionld; 12&fl; Math 1325 Business Calculus 320, 330. 335 Fall 2016 Homework: HW 8 (Review 11.1 through 13.4) Score: 0 of 1 pt 22 of 25 (24 complete) v 13.2.17 Find the x-values of all points where the function has any relative extrema. Find the value(s) of any relative extrema. 8 3 49 x2-6x +11 f(x) Select the correct choice below and, if necessary, fill in any answer boxes within your choice. O A. There are no relative maxima. The function has a relative minimum of at x (Use a comma to separate answers as needed.) O B. The function has a relative maximum of at x and a relative minimum of at x (Use a comma to separate answers as needed.) O c. There are no relative minima. The function has a relative maximum of atx. (Use a comma to separate answers as needed.) O D. There are no relative extrema. Click to select and enter your answer(s) and then click Check Answer. All parts showing Clear All

Explanation / Answer

f(x) = (8/3)x^3 - (49/2)x^2 - 6x + 11

f'(x) = 8x^2 - 49x - 6

f'(x) = 0 means 8x^2 - 49x - 6 = 0

x = [-b ± (b^2 - 4ac}/2a

x = [49 ± (49^2 - 4 * 8 * -6}/2 * 8)

x = {-0.12, 6.245} are the critical points

f"(x) = 16x - 49

f"(x) < 0 for x = -0.12 and f"(x) > 0 for x = 6.245

So, f(x) has a relative maximum at x = -0.12 and a relative minimum at x = 6.245

The relative maximum is f(-0.12) = 11.363 and the relative minimum is f(6.245) = -332.49