What is the minimum value of 3 cosx + 4 sinx + 8?

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+2 Mathematics Introduction to Trigonometry

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Ankit Agrawal

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f(x) = 3cosx + 4sinx + 5 f '(x) = -3sinx + 4cosx 0 = -3sinx + 4cosx 3sinx = 4cosx tanx = 4/3 x = 0.927 + npi radians for all integers, n f ''(x) = -3cosx - 4sinx f ''(0.927) = -5 0 so a minimum occurs at x = 4.069 f(0.927 + pi) = f(4.069) = 0
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f(x) = 3cosx + 4sinx + 5 f '(x) = -3sinx + 4cosx 0 = -3sinx + 4cosx 3sinx = 4cosx tanx = 4/3 x = 0.927 + npi radians for all integers, n f ''(x) = -3cosx - 4sinx f ''(0.927) = -5 < 0 so a maximum occurs at x=0.927 f ''(0.927 + pi) = 5> 0 so a minimum occurs at x = 4.069 f(0.927 + pi) = f(4.069) = 0 read less
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