Question

    The second derivative of y = tan⁻¹ x at x = 1

    is:
    A -1/2 Correct Answer Incorrect Answer
    B 1/2 Correct Answer Incorrect Answer
    C 2 Correct Answer Incorrect Answer
    D 1 Correct Answer Incorrect Answer

    Solution

    To find the second derivative of y = tan⁻¹x at x = 1. y = tan⁻¹x dy/dx = 1/(1 + x²) d²y/dx² = -2x/(1 + x²)² At x = 1: d²y/dx² = -2(1)/(1 + 1)² = -2/4 = -1/2

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