Question

Use the given function and the given interval to complete parts a through c. лл f(x) = sin 2x on a. Find the critical point(s) off on the given interval. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The critical point(s) occur(s) at x = (Use a comma to separate answers as needed. Type an exact answer, using a as needed.) B. There are no critical points off on the given interval. b. Determine the absolute extreme values off on the given interval when they exist. What is/are the absolute maximum/maxima off on the given interval? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The absolute maximum/maxima is/are at x = | (Use a comma to separate answers as needed. Type an exact answer, using a as needed.) B. There is no absolute maximum off on the given interval. What is/are the absolute minimum/minima off on the given interval? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The absolute minimum/minima is/are atx=| (Use a comma to separate answers as needed. Type an exact answer, using a as needed.) O B. There is no absolute minimum off on the given interval. c. Use a graphing utility to confirm your conclusions. Determine which graph represents f(x). Choose the correct answer below. OA. OB. C. OD. 2 A o ó Q n л 2 LY IN 2 2

Answer 1

Soin : f(x) sin 2x on [ ] ) . (0) ) 2. Cos 2x ... (a) =0 2 os 2x = 0 ㅋ 2x = N. 2. 12 - TT are coitical points of of f(n) - I - N 2. + Now, at x = TO sin ( 다. - T. 4 0 2. () f( at a= 4 t 10 sin ㅍ 正 4 at n= F 4 2 2 - O + ) sin (-o) sin (D) at x = 나 ) - 20 ) 2. - : The absolute maximum is af Me T 4 & The absolute minimum is ~1 at Le TT 4 (4.1) option c -0.5 -2/3 -ITA -13 -1/6 6 13 /2 20/3 0.5 (-4, -1)