Question

Use the first derivative test to determine the location of each local extremum and the value of the function at this extremum. - 2x f(x) = x 6 Identify the location and function value of the maximum of the function, if any. Select the correct answer below and, if necessary, fill in any answer boxes within your choice. O A. The function has a local maximum of at x = (Use a comma to separate answers as needed. Type exact answers in simplified form.) OB. The function does not have a local maximum.

Answer 1

* gicas Given that! f(2)=xe-22 Now & (xe 2x) 2. &ce-22) +e-29 ca = x.e-2% (-2) + e-29 1 - for e-2% (-2x+1) critical points we have: f'(an- (–2x+1) = 0 0 e- 22 ov 2= 2 We draw sign diagram for f'cas ++++++ #t 2 The 22 function has local maximum at 2 / 2 The maximum value bei huhe The function has a local maximum of 1 at az A. ze 2 - frao - 254?+ 7002 – 2787 drow f'(X) = (-2522+ 700x - 2787) = (-25; 27 + 700) = 6 502 + 700) so, é casa soat 700 for maximum profiti f'canzo -50%+ 700=0 OY x= 14

an the year 2014 local maximum Profit oceur. 6) maximum Profit be! -25 (14)+700.14 - 2787 = 2113 The manimum Profit was 2113 f(0) = 3x²+4841 f'(x) = A ( 3x3+4x+1) 9x²+4 f" ca- I h (9x²+4) - g-22 - 18 We draw sign diagram for f" (2) tttttt @e on & casa The function is concave uparand on: 1o,0) and Con care downward 0,0 f(x) = 355 de Gas) 5 2 (2-5)? 10 Ta-53 We draw sign diagram for f"(*): =+ 5 11 tttt ++ A. The function is concave and concave down wand upward on:\(5,0) on : 1-2,5)