MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
Consider the function h(x)=sinx−xcosx defined on the interval 0<x<2π.
(i) Show that h′(x)=xsinx and hence find all values of x in (0,2π) for which h′(x)=0.
(ii) Obtain an expression for h′′(x).
(iii) For each stationary point found in part (i), decide whether it is a point of local maximum or local minimum. Write the corresponding ordered pairs (x,h(x)) using exact values.
(iv) State which, if any, of these stationary points gives the greatest value of h on (0,2π).