AP

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

Problem

Let H(x)=x4−4x2+3sin⁡x−2cos⁡xH(x)=x^{4}-4x^{2}+3\sin x-2\cos x. (i) Find H′(x)H'(x). (ii) Calculate the slope of the tangent to the curve y=H(x)y=H(x) at x=π4x=\dfrac{\pi}{4}. (iii) Obtain the equations of the tangent and the normal to the curve at the point corresponding to x=π4x=\dfrac{\pi}{4}.

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