The height (in metres) of water in a tank at time seconds is given by h(x)= x x x+4

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

Problem

The height hh (in metres) of water in a tank at time xx seconds is given by h(x)=xsin⁡xx+4.h(x)=\dfrac{x\sin x}{x+4}. Answer the following. (i) Determine the rate of change of height with respect to time, dhdx\dfrac{dh}{dx}. (ii) Hence calculate the rate of change of height at x=πx=\pi seconds, correct to three decimal places.

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