For the function :

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

For the function p(x)=x3sin⁡xp(x)=x^{3}\sin x: (a) Determine p′(x)p'(x), leaving your final answer with powers of xx collected and a single trigonometric factor in each term. (b) Factorise p′(x)p'(x) completely. (c) Show that p′(x)=x2(3sin⁡x+xcos⁡x)p'(x)=x^{2}(3\sin x + x\cos x) and hence find all xx in 0≤x≤2π0\le x\le 2\pi for which the tangent to y=p(x)y=p(x) is horizontal.

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