Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

darkigloo Group Title

If f(x)=(x^2)(e^x) then f is decreasing for all x such that A. x<-2 B. -2<x<0 C. x>-2 D. x<0 E. x>0

  • 6 months ago
  • 6 months ago

  • This Question is Closed
  1. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Calculus or algebra?

    • 6 months ago
  2. darkigloo Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    calculus

    • 6 months ago
  3. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Ok cool stuff. So do you know how to find the derivative. The derivative is the function that tells if the original function is decreasing or increasing.

    • 6 months ago
  4. darkigloo Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    i think the derivative is e^x(x^2+2x)

    • 6 months ago
  5. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    that is right So when is the derivative 0 (this is to find when the function is doing neither increasing or increasing) I'm asking this: solve e^x(x^2+2x)=0

    • 6 months ago
  6. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    e^x is never 0

    • 6 months ago
  7. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    So you are basically looking at solving x^2+2x=0 right now.

    • 6 months ago
  8. darkigloo Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    x=0 x=-2

    • 6 months ago
  9. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    ok great. Now lets check the intervals around those numbers to see if we have f'>0 (which means f is increasing) or if we have f'<0 (which means f is decreasing) So what I'm asking you to do is look at the interval (-inf,-2) Take a number from this set and see if f'>0 or <0. Then we will also check the set of numbers (-2,0) and also check (0,inf)

    • 6 months ago
  10. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    we have three intervals to check.

    • 6 months ago
  11. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    when ever you plug in a number into e^x all you need to know is that the output will always be positive

    • 6 months ago
  12. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    So again looking at just x^2+2x

    • 6 months ago
  13. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    A number from the group (-inf,-2), we could choose -4. (-4)^2+2(-4)=a positive number>0 so on this interval it is increasing. Now you check (-2,0).

    • 6 months ago
  14. darkigloo Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    for (-2,0) its negative. for (0,-inf) its positive. So the answer is B. -2<x<0 right!? :D

    • 6 months ago
  15. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    that is right

    • 6 months ago
  16. darkigloo Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    thanks. and for the e^x...that is always positive?

    • 6 months ago
  17. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    any positive number raised to any power will always be positve

    • 6 months ago
  18. darkigloo Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    ok. thank you.

    • 6 months ago
  19. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1393014251807:dw|

    • 6 months ago
  20. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Like you can also look at the graph if you want it gets closer to 0 as we approach negative infinity but never touches or goes below

    • 6 months ago
  21. darkigloo Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    ohh right...i'll have to remember that graph. thanks :)

    • 6 months ago
  22. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    good luck with your calculus

    • 6 months ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.