Question

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?

Answer 1

@saseal

Answer 2

you mean \(s(t) = te^t\) ??

Answer 3

I suppose, I just copied the question honestly. @IrishBoy123

Answer 4

if you do mean: \(\large s(t)=te^t\)

then

\(\large v(t) = \dot s(t)=\frac{d}{dt}( te^t)\)

use product rule and set it to zero to find when the things is at rest

Answer 5

so find the derivative?

Answer 6

yes!

Answer 7

I tried doing what we did but that didn't work, but doing what he just said makes sense. I got 0 as a solution

Answer 8

maybe your function is like this:
\[\Large s\left( t \right) = t{e^{ - t}}\]

Answer 9

sorry, if I compute the first derivative, I got this:
\[\Large \frac{{d\left( {t{e^t}} \right)}}{{dt}} = \left( {t + 1} \right){e^t}\]

Answer 10

so we have to solve this algebraic equation:
\[\Large \left( {t + 1} \right){e^t} = 0\]

Answer 11

I got -1 as a solution

Answer 12

that's right!

Answer 13

Awesome! Thank you for your help!!

Answer 14

:)