What is the maximum value of f(x) = sin(x) + cos(x)? (Hard)
Answer and explanation
Correct answer: C. root 2
- Step 1: Express as R cos(x - alpha) where R = sqrt(1^2 + 1^2) = root 2. Step 2. Since the maximum of cos(x - alpha) is 1, the maximum value is root 2 1 = root 2. Answer: root 2. Why not the others:* 2 simply sums maximums 1 + 1 (which cannot occur simultaneously); 1 is the individual maximum; root 3 corresponds to coefficients 1 and root 2.
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