Mathematics

Problem

For the curve

y=x\cos x

, consider the interval

0<x<2\pi

. a. (i) Obtain

\dfrac{dy}{dx}

. b. (ii) Determine all values of

x

in the given interval for which the tangent to the curve is horizontal. c. (iii) For each value of

x

found in part (ii), state whether the curve is rising or falling immediately to the right of that point, giving reasons based on the derivative.