Question

Summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of f(x) = + 2x-15 ² Summarize the pertinent information obtained by analyzing f(x). O A. f(x) is decreasing on (-00, 0) and (0, 15) and increasing on (15,..). O B. f(x) is increasing on (-00, 0) and (15, 0o) and decreasing on (0.15). OC. f) is decreasing on (-0, 0) and (15,00) and increasing on (0, 15). OD. f(x) is increasing on (-0,0) and (0, 15) and decreasing on (15,00) IO A. There is a local maximum at x = 0. O B. There are no local extrema. OC. There is a local minimum at x = 0. OD. There is a local minimum at x = 15. O E. There is a local maximum at x = 15 Summarize the pertinent information obtained by analyzing OA 45 Concave upward on (-00, 0) and ž c0) Concave downward on (0, 45 2

Answer 1

US 112 W +23--15 f(u) = Differentiating with respect to a we have (WV+21-15) da (m2) u2 dan 42+24-15) f1co) หฯ Ox, f(m) 22 (2x+2) - (+22-15) (26) u4 24² +22²_213_un²+300 or, fl(W) = us (1) 30-2u Oy, f(n) = 301-21² NY 13 And furn) ca (30-21) – (30-2%) (23) no 23 (-2) (30-22) (342) ut -243_gon²+ 643 no 443_9012 or fl(n) no 41-90 un or flex) 44 fen) is increasing if fl (1) Yo => 30-2470 13 It's possible if both 30-2x 70, u370 implies, ocu15, That is fon) is increasing on 6.0,15)

+ (n) is deorening if flon) Lo => 30-20 KO 13 or uLO. It is possible if Cases, 30-2x<0, 4370 Or. Soyez 30-270, ufo. le if ny15 ise, if he (-8,0) (15,4) Therefore few is deureooing on (-1,0) 0115,«0) To find eritical points, fu (n) = 0 gives. point. So, x=15 is a critical 30-21 0 => u=15. Hence at u=15. 43 30 co et u=15, f(n) = 4.15-90 (15)4 f (1) attains its maximum value. ИЧ Now, f(x) is concave upward if pll (n).yo => 428-9070 ay uy 45 ie, ue ( 45 ) fox) is concave downward if fil(a) <o - 41-90 20 nu 2 => uL 45 and uto je, me (-0,0) 0(0,43)

have, This summarizing information from flen) we c. f(n) is deoreening on (-26,0) omd (15.%) and inore on (0,15) noreasing 7 Do There is a local maximum at n=15. And summarizing information from flca) we have. Concave uproard on (45,-), concave downwand on (-0,0) and (0,45 2