A particle moves along a straight line with a differentiable position function s(t) on the closed interval [a,b]. Which of the following procedures will always identify the time at which the particle is farthest to the right during the interval?
a) Evaluate s′(t)=0 for t in (a,b) and choose the time at which s′′(t)<0.
b) Evaluate s(t) only at the endpoints t=a and t=b; the greater of the two values occurs at the desired time.
c) Evaluate s(t) at every critical number where s′(t)=0 or is undefined in (a,b) and at the endpoints t=a and t=b; the greatest of these values occurs at the desired time.
d) Determine the time in (a,b) at which s′(t) attains its greatest positive value; that time gives the farthest right position.