Quantcast

A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

livelaughlilz

  • 2 years ago

what is the minimum value of 7^(x^2-4x+7)

  • This Question is Closed
  1. saifoo.khan
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\Large 7^{x^2-4x+7}\]Like this?

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

    yes

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

    @mathmate @UnkleRhaukus

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

    Minimum value should be there where dy/dx = 0.

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

    what do you mean by the "d"?

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

    In other words minimum value occurs where the derivative of the function is equal to zero.

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

    isn't derivatives calculus? i haven't learned that yet and i don't think we're expected to know it to solve this problem

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

    http://www.mememaker.net/static/images/templates/14288.jpg

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

    haha i was thinking about it and wouldn't it be one over infinity? because if x^2-4x+7 was negative infinity than 7^(x^2-4x+7) would be 1/infinity

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

    Hint: 7^x is an increasing function. So if we minimize x, 7^x is also a minimum.

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

    x^2-4x+7 cannot be at -inf. It is a parabola concave upwards.!

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

    And are we going to try that by trial and error? @mathmate

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

    No, we need to simply find the vertex of the parabola to find the minimum value of the parabola.

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

    Howw??

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

    Good point!] @livelaughlilz can you take it from here?

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

    Completing the squares will do the job.

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

    yeah the vertex of the parabola is (2,3)

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

    (x-2)^2=y-3

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

    x^2-4x+7=(x-2)^2+3 so the vertex is at (2,3)

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

    http://i1.kym-cdn.com/entries/icons/original/000/009/993/tumblr_m0wb2xz9Yh1r08e3p.jpg

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

    Good job livelaughlilz! Speed+accuracy!

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

    I like his movies! :)

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

    oh so the answer is 343. the lowest value of x is 2, and if you plug it in you get 7^3=343

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

    Yes^ @livelaughlilz

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

    7^2 = ???

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

    @mathmate : haha, nice. My brother just love his movies. i don't. :/

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

    Nevermind, I was out of my mind. Yes, 7^3=343

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

    You were thinking about Jackie Chan. :D

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

    As a sidenote @mathmate, you can find the x-coordinate of the vertex using the formula \[v_x=\frac{-b}{2a}\]

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

    Thank you for the defence, even though it was a lame one! Good thinking! :)

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

    I simply love this method. Satellite73 taught me this. -b/2a

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

    to add onto @KingGeorge the y-coordinate of the vertex is -[(b^2-4ac)/(4a)]

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

    Thank you @KingGeorge, my memory is limited and sometimes defective. But thanks for the shortcut anyway!

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

    you can figure all that out by completing the square of y=ax^2+bx+c

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

    and making y=ax^2+bx+c into vertex form

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

    Actually I know the -b/2a part, that's how I get to do the completing the square. It's just I never managed to memorize the -[(b^2-4ac)/(4a)] part.

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

    well b^2-4ac is also the discriminant...

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

    @livelaughlilz is a boss at this.

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

    Perhaps from this time on I will remember. Practice makes perfect! :)

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

    Actually what I do is finding it by c-(b/2a)^2, which is exactly what we do when we complete the square.

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

    oh

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

    i'm going to close this question now. thanks everyone!

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

    See you all!

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

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy

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.