Answer the questions below about the concepts of velocity and speed for motion in the plane. Assume all component functions are differentiable on an open interval containing t=c.
(a) Describe clearly the distinction between the velocity vector of a particle and the particle’s speed at a given instant.
(b) Suppose a particle’s velocity vector is v(c)=⟨0,0⟩ at an isolated instant t=c. Explain whether t=c must represent a local extremum of the particle’s speed. Support your conclusion with reasoning that references differentiability and appropriate definitions, but without explicit computation for a particular function.