Find the intervals on which f is increasing and decreasing. f(w) = - cos w ( - w2 + 2) - 2w sin w on 2' 2 . . . Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. The function f is increasing on the open interval(s) and decreasing on the open interval(s) O A. (Simplify your answer. Type an exact answer, using it as needed. Type your answer in interval notation. Use a comma to separate answers as needed.) The function f is decreasing on the open interval(s) . The function f is never increasing. O B. (Simplify your answer. Type an exact answer, using it as needed. Type your answer in interval notation. Use a comma to separate answers as needed.) The function f is increasing on the open interval(s) The function f is never decreasing. O C. (Simplify your answer. Type an exact answer, using it as needed. Type your answer in interval notation. Use a comma to separate answers as needed.) O D. The function f is never increasing or decreasing.Determine the intervals on which the following function is concave up or concave down. Identify any inflection points. f(0) = 20 sin 0 + 4 cos 0, on (0,2T) . . . SCICUL LIC WITGUL WITVIVE UCIVW aIIIIII III TIC alISWel UVA(CS) IV WITIPICLE youI WIIVICE. (Simplify your answer. Type your answer in interval notation. Use a comma to separate answers as needed. Use ascending order.) A. The function is concave down on (0,It) and concave up on (It, 2n) . O B. The function is concave down on and the function is never concave up. O C. The function is concave up on and the function is never concave down. Identify all the inflection points, c. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. C= (Use a comma to separate answers as needed.) O B. There are no inflection points.The graph of f' on the interval [3,8] is shown in the figure to the right. + Complete parts (a) through (f) below. X . . . a. Find the largest possible open interval(s) on which f is increasing, and the largest possible open interval(s) on which f is decreasing. Select the correct choice below and, if necessary, fill in the answer box(es) within your choice. O A. The function is increasing on the open interval(s) and decreasing on the open interval(s) (Simplify your answer. Type your answer in interval notation. Use a comma to separate answers as needed.) O B. The function is decreasing on the open interval(s) . The function is never increasing. (Simplify your answer. Type your answer in interval notation. Use a comma to separate answers as needed.) O C. The function is increasing on the open interval(s) . The function is never decreasing. (Simplify your answer. Type your answer in interval notation. Use a comma to separate answers as needed.) O D. The function is never increasing nor decreasing.A typical population curve is shown in the figure. The population is small at t= 0 and increases toward a steady-state level PA K+2 called the carrying capacity. The population of a species is given by the function P(t) =- -, where t 2 0 is measured in years Carrying capacity 12 + b and K and b are positive real numbers. Complete parts (a) through (c) below. Population P = f(1) Inflection point O Time . . . a. With K = 450 and b = 30, what is lim P(t), the carrying capacity of the population? 1 00 lim P(t) = (Simplify your answer.) 1-+ 00