Find the maximum and minimum values of $f(x) = x + \sin 2x$ on $[0, 2\pi]$.
Step-by-Step Solution
$f'(x) = 1 + 2\cos 2x = 0 \Rightarrow x = \pi/3, 2\pi/3, 4\pi/3, 5\pi/3$. [1.0 Mark]
Evaluate $f(0)=0, f(2\pi)=2\pi$. [1.0 Mark]
Maximum value $= 2\pi$, Minimum value $= 0$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Finding critical points in $[0, 2\pi]$: 1.0 Mark
Evaluating function at endpoints and critical points: 1.0 Mark
Evaluating maximum $= 2\pi$ and minimum $= 0$: 1.0 Mark
Correct Answer: