A particle moves along the x-axis with position function s(t) = xe^x. How many times in the interval [-5, 5] is the velocity equal to 0?

Question

One

Two

Three

more than three

Answer 1

The velocity function is the derivative of the position function.

To do the derivative xe^x, we need product rule. First * Derivative of second + Second * Derivative of first

s(t) = xe^x

v(t) = s'(t) = x*e^x + e^x * 1 = xe^x + e^x

Now we set v(t) = 0 and solve for x

xe^x + e^x = 0

Factor out e^x

e^x (x+1) = 0

Set each factor = 0

e^x = 0

e^x never equals 0

x+1 = 0

x = -1

The velocity is equal to 0 once between x = -5 and x = 5.