Zeros of a Cosine Product

★ 6/10trigonometry Extrema calculus Monotonicity

Problem

Let

f(x) = \left(x - \frac{\pi}{2}\right)\cos x + 1.

1. Discuss the monotonicity of $f(x)$ on the interval $[0, \pi]$ . 2. Determine, with proof, the number of zeros of $y = f(x)$ on the interval $\left[\dfrac{\pi}{2}, \dfrac{3\pi}{2}\right]$ .

Answer

Solution

Difficulty	6/10
Topics	trigonometry, Extrema, calculus, Monotonicity

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