A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

tmagloire1

  • one year ago

Given f '(x) = (x + 1)(6 + 3x), find the x-coordinate for the relative minimum on the graph of f(x). 0 −1 −2 None of these ---- http://prntscr.com/8bljw7

  • This Question is Closed
  1. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    do you know what \(y=(x+1)(6+3x)\) looks like?

  2. tmagloire1
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    a parabola

  3. tmagloire1
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    upward

  4. tmagloire1
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @satellite73

  5. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    a parabola that opens up, right and the zeros are?

  6. tmagloire1
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    -1 and -2

  7. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok good so lets draw a quick picture

  8. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1441157312300:dw|

  9. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    at \(x=-2\) the derivative goes from being positive (above the x axis) to negative (below the x axis) that tells you the function goes from increasing to decreasing at \(-2\) i.e. up and then down therefore \(-2\) is a relative max |dw:1441157412113:dw|

  10. tmagloire1
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    exactly what i drew. i got 1.5ish as a minimum but it wasn't an option so i wasn't sure if they were trying to trick me by putting -1 and -2

  11. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    no it has a relative math right at \(x=-2\) by a similar argument it has a relative min at \(x=-1\)

  12. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    at any rate the derivative has degree two, so the original function has degree 3 with positive leading coefficient|dw:1441157542119:dw|, so you have a good idea that it looks like this

  13. tmagloire1
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    you lost me..

  14. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok lets go slow then

  15. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    you know what the derivative looks like right?

  16. tmagloire1
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes

  17. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    and you know (or are supposed to be learning) that if the derivative is positive, then the function is increasing, and if the derivative is negative, tehn the function is decreasing

  18. tmagloire1
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes i learned that

  19. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok good now "positive" is a synonym for "above the x axis"

  20. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1441157806983:dw|

  21. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    that means on the interval \[(-\infty,-2)\] and \[(-1,\infty)\]the function is increasing

  22. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    not the derivative, the original function \(f\) also on \((-2,-1)\) the function is decreasing

  23. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    it goes up until it gets to -2, then it goes down that means -2 gives a relative MAX it goes down until -1, then it goes back up again that means -1 gives a relative MIN

  24. tmagloire1
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Ohh okay so you just us eincreasing/decreasing rules/ i understand thanks

  25. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yw

  26. tmagloire1
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Can you help me with my second question as well?

  27. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    sure but i didn't see it

  28. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh now i do take the derivative what do you get?

  29. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i hope you get \[t^2-15t+50\]

  30. tmagloire1
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    For the derivative I got :t^2-50t+50

  31. tmagloire1
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oops i meant 15

  32. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok so your job is to solve \[t^2-15t+50<0\]

  33. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    because if the derivative is negative, it is moving to the left

  34. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    fortunately for you this factors, so it should be easy

  35. tmagloire1
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    t<5

  36. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    is it clear how to solve that, or no?

  37. tmagloire1
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    t>10

  38. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i think you solved for where it is positive

  39. tmagloire1
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    How am I supposed to solve this then? The two intervals i got were those

  40. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    it is zero at 5 and 10 right?

  41. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1441158937764:dw|

  42. tmagloire1
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes i got this

  43. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    since this parabola opens up, it is negative between the zeros and positive outside of them i.e negative on \((5,10)\)

  44. tmagloire1
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    is moving left another name for negative?

  45. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    moving to the left = derivative is negative

  46. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i.e. the velocity is negative

  47. tmagloire1
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so 5<t<10 would be correct?

  48. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes

  49. tmagloire1
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Thank you for explaining them to me! I appreciate it!

  50. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

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.