MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
For the curve y=xcosx, consider the interval 0<x<2π.
(i) Obtain dxdy.
(ii) Determine all values of x in the given interval for which the tangent to the curve is horizontal.
(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.