Consider the function .

MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Consider the function F(x)=x4−4x3+x2+2sin⁡x−3cos⁡xF(x)=x^{4}-4x^{3}+x^{2}+2\sin x-3\cos x. (i) Differentiate F(x)F(x) with respect to xx and simplify the result. (ii) Factorise completely the polynomial part of F′(x)F'(x). (iii) Evaluate F′ ⁣(π2)F'\!\left(\dfrac{\pi}{2}\right), writing your answer in exact form.

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