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 x-coordinate 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(2-1) = 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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