Posted by Yoona on Monday, February 13, 2012 at 7:28pm.
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, Monday, February 13, 2012 at 7:38pm
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.
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