Question

Consider the function on the interval (0, 2). f(x) = sin(x) cos(x) + 8 (a) Find the open interval(s) on which the function is increasing or decreasing. (Enter your answers using interval notation.) increasing decreasing (b) Apply the First Derivative Test to identify all relative extrema. relative maxima (x, y) = (smaller x-value) (larger x-value) (X,Y)= (x, y) = (1 (x, y) = relative minima (smaller x-value) (larger x-value)

Answer 1

F(x) = sinx loss +8 flona losse sina col o = (x2) So I(lter) = x2 Q x = (202) H so x = T 48 51 2 h חר 4 Ex:G9IMS CASIO 나. تم - br IT 3T ST TA 4 G u 4 at x = T. 9 flm so on x + 10,844) V ( 317 SHU (17/12) Hence insearing on given interval. ::8114920 on XA (My, 3174) U15/,, "%) Hence decressing on given interval $(5/4)= - * 1 to 17 / F1369,75 Ja Beste at xo s/ F (S) = 2 x ( 3 ) +8 F(*1%) relative minxima (1/4, 17) & (S/E) > 31 5 XIBE:15 2 15 at x 2 나 1 +8 ,کی رک 2 selisive minima 13 / 1124) & (T/ 1156)