Jeeify
MCQMediumJEE Main 2023 · 10 April, Shift 2Applications of Derivatives (Monotonicity, Extrema)

Mathematics Question from JEE Main 2023 · 10 April, Shift 2

Let g(x)=f(x)+f(1−x)g(x) = f(x) + f(1 - x) and f′′(x)>0f''(x) > 0 for all x∈(0,1)x \in (0, 1). If gg is decreasing in the interval (0,α)(0, \alpha) and increasing in the interval (α,1)(\alpha, 1), then tan⁡−1(2α)+tan⁡−1(1α)+tan⁡−1(α+1α)\tan^{-1}(2\alpha) + \tan^{-1}\left( \frac{1}{\alpha} \right) + \tan^{-1}\left( \frac{\alpha + 1}{\alpha} \right) is equal to:

  • A

    5π4\frac{5\pi}{4}

  • B

    π\pi

  • C

    3π4\frac{3\pi}{4}

  • D

    3π2\frac{3\pi}{2}

Answer & step-by-step solution

Sign in to reveal the correct answer, the full step-by-step solution, and the common mistakes for this question.

Sign in to see the solution

Practice more Applications of Derivatives (Monotonicity, Extrema) questions

Get unlimited AI-adaptive practice, mastery tracking, and an AI tutor that explains every step - free to start.

Start free trialMore on Applications of Derivatives (Monotonicity, Extrema)

Related questions