`f(x) = 6sin(x) + cot(x), -pi<=x<=pi` Produce graphs of `f` that reveal all the important aspects of the curve. In particular, you should use graphs of `f'` and `f''`

Expert Answers
gsarora17 eNotes educator| Certified Educator


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



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)

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