## zeesbrat3 one year ago 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?

1. zeesbrat3

@saseal

2. IrishBoy123

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

3. zeesbrat3

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

4. IrishBoy123

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

5. zeesbrat3

so find the derivative?

6. Michele_Laino

yes!

7. zeesbrat3

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

8. Michele_Laino

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

9. Michele_Laino

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

10. Michele_Laino

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

11. zeesbrat3

I got -1 as a solution

12. Michele_Laino

that's right!

13. zeesbrat3

Awesome! Thank you for your help!!

14. Michele_Laino

:)