Posted by Yoona on .
3. Let f be the function defined by f(x)=ln(2+sinx) for pi<=x<=2pi
a. Find the absolute maximum value and the absolute minimum value of f. Show the analysis that leads to your conclusion.
b. Find the xcoordinate of each inflection point on the graph of f. Justify your answer.

calculus 
Reiny,
f'(x) = cosx/(2+sinx)
for max/min,
cosx/(2+sinx)= 0
cosx = 0
x = π/2 or x = 3π/2
when x =π/2
f(π/2) = ln(2 + 1) = ln 3
when x = 3π/2
f(3π/2) = ln(21) = ln 1 = 0
so which is max and which is min ?
for pts of inflection, find
f''(x), then set that equal to zero
I suggest the quotient rule.