Question
Download Solution PDFComprehension
Direction : Consider the following for the items that follow :
Let f(x) = cos2x + x on [-π/2, π/2].
What is the greatest value of f(x)?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
Given:
f(x) = cos2x + x on [-π/2, π/2].
⇒ f'(x) = – 2 sin 2x + 1
For maxima and minima, f'(x) = 0
Sin2x = 1/2
x = π/2 or 5π/12 (not in interval)
So maximum value of f(x) occurs at x = π/12
\(f(\frac{\pi}{12}) = cos\frac{\pi }{6}+ \frac{\pi }{12} \)
= \(\frac{\sqrt3}{2}+\frac{\pi}{12}\)
∴ Option (b) is correct.
Last updated on May 30, 2025
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