A point on a rotating wheel of radius is located on a spoke that makes an angle (in…

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

Problem

A point

P

on a rotating wheel of radius

2\,\text{m}

is located on a spoke that makes an angle

x

(in radians) with the horizontal. The vertical displacement

y

(in metres) of

P

from the centre of the wheel is given by

y=\dfrac{2\sin x}{x}

for

x\neq0

. (i) Obtain the expression for

\dfrac{dy}{dx}

in terms of

x

. (ii) Calculate the rate of change of

y

with respect to

x

when

x=0.2\,\text{rad}

. Give your answer correct to four decimal places. (iii) Interpret the sign of the value found in part (ii) with reference to the motion of point

P

Related theory

Interpreting Derivatives
Differentiation Rules
Derivatives of standard functions via chain rule

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