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math

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I need to use calculus to solve this word problem:
Find all maximum and minimum values for f(x)= sin(x)+ cos(x) on [0, 2(3.14)]

How do I do it?

  • math - ,

    f(x) = sinx + cosx , 0 ≤ x ≤ 2π
    f ' (x) = cosx - sinx
    = 0 for a max/min
    cosx - sinx = 0
    sinx = cosx
    sinx/cosx = 1
    tanx = 1
    x = 45° or 225°
    x = π/4 or x = 5π/4

    f(π4) = √2/2 + √2/2 = √2
    f(5) = -√2/2 - √2/2 = -√2

    the max is √2, the min is -√2

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