Quantcast

A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

burhan101

  • 2 years ago

Determine the maximum and minimum. f(x)= 1+ (x+3)² ; -2<x<6

  • This Question is Closed
  1. TuringTest
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    how does one find maxima and minima of a function?

  2. burhan101
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    first find the derivative f'(x)= 2x+6

  3. Jhannybean
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    sure it isnt \(-2 \le x\le 6\) ?

  4. burhan101
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes @Jhannybean

  5. TuringTest
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    and what do we do with the derivative to find max and min (also known as critical points)?

  6. burhan101
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    x=-3

  7. burhan101
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    f(-3)=1 f(-2)=2 f(6)=82

  8. TuringTest
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the critical points are found when the derivative is equal to zero (unless they are at the endpoints of the function, which you don;t need to worry about if you have no greater than or equal sign)

  9. TuringTest
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \(f'(x)\)=0

  10. burhan101
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes i calculated it that way x=-3

  11. burhan101
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    and sorry i forgot to put \[-2 \le x \le 6\]

  12. TuringTest
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    and you still don't know the answer?

  13. TuringTest
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    you want the max and min values of the function; when is f(x) largest and smallest according to your calculations?

  14. burhan101
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes i get 6,82 as my max and -3,1 as my min BUT my answer key says maximum:82, minimum:6

  15. Jhannybean
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Use the points you tested to find your highest and lowest values.

  16. TuringTest
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    -3 is not an option for x, but that leaves x=-2, which still does not give 6... so I still do not see how that can be right

  17. burhan101
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @TuringTest so there a problem with the ansswerkey?

  18. TuringTest
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    It's the only thing I see possible, and it certainly wouldn't be the first time I've seen the answer key be wrong.

  19. TuringTest
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    http://www.wolframalpha.com/input/?i=plot+f%28x%29%3D+1%2B+%28x%2B3%29%C2%B2+%3B+-2%3Cx%3C6 how 6 is a minimum in this graph is beyond me

  20. burhan101
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so what would the local minimum be?

  21. TuringTest
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the local mina and max are also the global min and max in this case

  22. Jhannybean
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    \[\large f(x) = 1+(x+3)^2 \ \ , \ -2 \le x \le 6\]\[\large {f'(x) = 2(x+3)(1) =0 \\ f'(x)= 2x+6=0 }\]\[\large x = -3\] Test your end points and your critical points with the help of The Extreme Value Theorem. 1. your function is continuous since it's a polynomial 2. x=-3 does not fall between the interval [-2,6] so cannot be tested. 3.Test your end points \[\large {f(-2) = 1+((-2)+3)^2 = 2 }\]\[\large f(6) = 1+ ((6)+3)^2= 82\] Ab max = (-2,2) Ab Min = (6,82)

  23. TuringTest
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I agree, and think the answer key is wrong. I would guess it a typo where someone wrote the x=6 which corresponds to the max instead of the min. It really is not that uncommon; books can be mistaken :p

  24. Jhannybean
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Sorry, Ab max = (6,82), Ab min = (-2,2) hehehe

  25. TuringTest
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    well then we all agree :) nice job solving it though!

  26. Jhannybean
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    thanks! I typoed earlier :c

  27. TuringTest
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    no worries, it happens to the best of us :P

  28. 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.