Calculus: Early Transcendentals, Chapter 4, 4.6, Section 4.6, Problem 7

f(x)=6sin(x)+cot(x)
See the attached graph and link(different range), f(x) is in Red color, f' is in Blue color and f'' is in Green color.
From the graph, Vertical Asymptotes at x=0, x=pi , x=-pi
f is decreasing on the intervals (-pi,-1.40) , (-0.40,0) ,(0,0.40) and(1.40,pi)
f is increasing on the intervals(-1.40,-0.40) and(0.40,1.40)
Local minimum f(-1.40) ~~ -6 , f(0.40) ~~ 4.75
Local maximum f(-0.40) ~~ -4.75 , f(1.40)~~ 6
f'(x)=6cos(x)-csc^2(x)
f''(x)=-6sin(x)+2csc^2(x)cot(x)
From the Graph,
function is Concave up on the intervals at about (-pi,-0.80) and (0,0.80)
function is concave down on the intervals about (-0.80,0) and(0.80,pi)
Inflection points at about (-0.80,-5.25) and (0.80,5.25)