Extremes on a Moving Curve

★ 8/10functions Extrema calculus Monotonicity

Problem

The function $f(x) = ax^3 + bx^2 + cx + d$ has local extrema at the two points $O$ and $A$ , where $O$ is the origin and $A$ lies on the curve

y = x^2\sin x + x\cos x, \qquad x \in \left[\frac{\pi}{3}, \frac{2\pi}{3}\right].

Find the maximum possible slope of a tangent line to $y = f(x)$ .

Answer

Solution

Difficulty	8/10
Topics	functions, Extrema, calculus, Monotonicity

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