On which of the following intervals is the function f(x) = x¹⁰⁰ + sin x - 1 strictly decreasing?
On which of the following intervals is the function f(x) = x¹⁰⁰ + sin x - 1 strictly decreasing?
- A. (0, 1)
- B. (π/2, π)
- C. (0, π/2)
- D. None of these
Answer: D) None of these
Explanation: f'(x) = 100x⁹⁹ + cos x. In (0, 1) and (0, π/2), both terms are positive. In (π/2, π), 100x⁹⁹ > 1 and cos x ∈ [-1, 0), so f'(x) > 0. It is never strictly decreasing on these intervals.
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