Please help: calculus prob

Question

A particle moves along the x-axis with position function s(t) = e^sin(x). How many times in the interval [0, 2π] is the velocity equal to 0? 

Options:

1. one
2. two
3. three
4. more than three

Answer 1

Since:

s(t) = e^sin(t),

v(t) = s'(t),

(d/dt) e^u = e^udu, and

(d/dt) sin(t) = cos(t).

Then v(t) = cos(t)e^sin(t) and equals zero when cos(t) = 0,

namely, when t = π/2 and 3π/2.