A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

The figure below shows the graph of f ′, the derivative of the function f, on the closed interval from x = −2 to x = 6. The graph of the derivative has horizontal tangent lines at x = 2 and x = 4. Find the x-value where f attains its absolute maximum value on the closed interval from x = −2 to x = 6. Justify your answer

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

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

    @Empty @IrishBoy123

  3. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1439314511563:dw|

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

    |dw:1439314520378:dw|

  5. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    what do you know about the relationship between first derivative and relative min/max ?

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

    wherever the first derivative = zero their is likely a max min , where the first derivative is negative and then positive the function is concave down and the inverse of that to indicate concave up

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

    umm thats pretty much it, am i missing something

  8. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    that looks good, look at the given graph of first derivative notice that the first derivative stays negative in the interval [-2, 5], this means the function is "decreasing" in this interval, yes ?

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

    yep

  10. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    we cannot have any max/min in the interval (-2, 5) since the function is continuously decreasing

  11. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    what about the point (5, 0) does that mean the function has a min or max at x=5 ?

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

    min

  13. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    good, since the first derivative is going form "negative" to "positive", the function will have a local minimum at x=5

  14. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    that essentially means, we do not have any local maximums in the interval (-2, 6)

  15. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    so the absolute maximum must occur at the boundary points

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

    x = 6!!

  17. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    how do you know ?

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

    well it just kept increasing after x = 4 so i figured it would be the highest , but i guess x=-2 could be just as high because we don't know what happened before x = -2 right?

  19. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Notice that the first derivative is "negative" in the interval (-2, 5) that means the actual function is "decreasing" in the interval (-2, 5)

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

    okay i see so your suggesting that because it decreased for such a long interval and then increased for such a short interval the maximum would be ant x = -2 is that what your saying?

  21. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Kindof! but thats not it, at this point, i do believe the function attains its maximum at x = -2

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

    okay well why do you suggest its x = -2?

  23. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1439315773571:dw|

  24. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    which area do you think is more black or red ?

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

    well grey obviously

  26. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    That means the actual function did not recover the fall yet

  27. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    so x=-2 is indeed the absolute maximum

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

    okay that makes sense

  29. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    If you're good with definite integrals, notice below : \[f(6)-f(-2) = \int\limits_{-2}^6f'(x)\,dx \lt 0\] that implies \(f(6)\lt f(-2)\)

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

    okay thanks for the help!

  31. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    yw

  32. 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.