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NDA 2 2024 Maths, question 85

Topic: Differential calculus

Passage · Q85 to Q86

Let f(x)=cos⁡2x+xf(x)=\cos 2x+x on [−π/2,π/2][-\pi/2,\pi/2].

Q85

What is the greatest value of f(x)f(x)?

  1. (a) 32−π12\frac{\sqrt{3}}{2}-\frac{\pi}{12}
  2. (b) 32+π12\frac{\sqrt{3}}{2}+\frac{\pi}{12}Correct answer
  3. (c) 32+π9\frac{\sqrt{3}}{2}+\frac{\pi}{9}
  4. (d) 32+π6\frac{\sqrt{3}}{2}+\frac{\pi}{6}

Solution.

Answer: (b) 32+π12\frac{\sqrt{3}}{2}+\frac{\pi}{12}

  1. Differentiate: f′(x)=1−2sin2x.
  2. In the interval the stationary points are π/12 and 5π/12.
  3. Evaluate these and the endpoints: f(π/12)=√3/2+π/12, f(5π/12)=−√3/2+5π/12, and f(±π/2)=−1±π/2.
  4. The largest is √3/2+π/12, option (b).