A particle moves along the x-axis so that at any time t≥0 its position is given by x(t)=te^-at, where a is positive constant. At what time t is the particles position farthest to the right?

Question

A particle moves along the x-axis so that at any time t ≥ 0 its position is given by x(t)=te^-at, where a is positive constant. At what time t is the particles position farthest to the right?

Answer 1

v(t) = x'(t) = e^-at - ate^-at= e^-at(1 - at) = 0, 1 - at = 0 and t = 1/a and we have max because left from t = 1/a v(t)> 0 and right of t = 1/a v(t) < 0