Homework Soursecosx2sinx a find all vertical asymptotes b find all local ma
cos(x)/[2+sin(x)]
a. find all vertical asymptotes
b. find all local max and min
c. on what interval is function increasing/decreasing
d. find all inflection points
e. what interval is concave down/ concave up?
a. find all vertical asymptotes
b. find all local max and min
c. on what interval is function increasing/decreasing
d. find all inflection points
e. what interval is concave down/ concave up?
Solution
cosx/2 + sinx
: there is no vertical asymptote
(2 + sinx)(-sinx) - (cosx)(cosx) = 0
-2 sinx - sinx*sinx - 1 + sinx*sinx = 0
sinx = -1/2
(sqrt[3]/2)(2 - 1/2) : sqrt[3]/3 : 1/3 local maxima
sinx + 1/2 > 0 gives you when it is rising (increasing) and rezst decreasing
d) do yourself .....
e) values of x where sinx = -1/2 divides the grpah . on one side it is concave and other side it is convex !!!
![cos(x)/[2+sin(x)] a. find all vertical asymptotes b. find all local max and min c. on what interval is function increasing/decreasing d. find all inflection poi](/WebImages/5/cosx2sinx-a-find-all-vertical-asymptotes-b-find-all-local-ma-982579-1761504506-0.webp "cos(x)/[2+sin(x)] a. find all vertical asymptotes b. find all local max and min c. on what interval is function increasing/decreasing d. find all inflection poi")
