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March 30, 2017

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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 - ,

    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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