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Find the maximum and minimum values of f(x) = 1 + 2 sin(x) + 3 cos²(x).

1. Maximum 17/3, minimum -1
2. Maximum 6, minimum 0
3. Maximum 17/3, minimum 0
4. Maximum 4, minimum -2

Correct answer: Maximum 17/3, minimum -1

Solution

Substituting gives a downward parabola g(t) = -3t² + 2t + 4 in t = sin x. The vertex at t = 1/3 gives the maximum 17/3; the minimum over [-1,1] is at the endpoint t = -1, giving -1.

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