A particle moves along a straight line with a differentiable position function on the…

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

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

(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.