A particle moves in the plane with velocity vector for

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

Problem

A particle moves in the plane with velocity vector

v(t)=\langle f'(t),g'(t)\rangle

for

a\le t\le b

. Which of the following procedures is MOST appropriate for identifying the time at which the particle attains its greatest speed on the interval

[a,b]

? (a) Set

|v'(t)|=0

, then compare the resulting

t

–values with the endpoints. (b) Set

f''(t)=0

and

g''(t)=0

, then test the resulting

t

–values and the endpoints. (c) Set

s'(t)=0

where

s(t)=|v(t)|

, then compare those critical numbers with the endpoints. (d) Set

f'(t)=0

and

g'(t)=0

, then test the resulting

t

–values and the endpoints.