anonymous
  • anonymous
what is the minimum value of 7^(x^2-4x+7)
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
saifoo.khan
  • saifoo.khan
\[\Large 7^{x^2-4x+7}\]Like this?
anonymous
  • anonymous
yes
saifoo.khan
  • saifoo.khan
@mathmate @UnkleRhaukus

Looking for something else?

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

More answers

saifoo.khan
  • saifoo.khan
Minimum value should be there where dy/dx = 0.
anonymous
  • anonymous
what do you mean by the "d"?
saifoo.khan
  • saifoo.khan
In other words minimum value occurs where the derivative of the function is equal to zero.
anonymous
  • anonymous
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
saifoo.khan
  • saifoo.khan
http://www.mememaker.net/static/images/templates/14288.jpg
anonymous
  • anonymous
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
mathmate
  • mathmate
Hint: 7^x is an increasing function. So if we minimize x, 7^x is also a minimum.
mathmate
  • mathmate
x^2-4x+7 cannot be at -inf. It is a parabola concave upwards.!
saifoo.khan
  • saifoo.khan
And are we going to try that by trial and error? @mathmate
KingGeorge
  • KingGeorge
No, we need to simply find the vertex of the parabola to find the minimum value of the parabola.
saifoo.khan
  • saifoo.khan
Howw??
mathmate
  • mathmate
Good point!] @livelaughlilz can you take it from here?
mathmate
  • mathmate
Completing the squares will do the job.
anonymous
  • anonymous
yeah the vertex of the parabola is (2,3)
anonymous
  • anonymous
(x-2)^2=y-3
mathmate
  • mathmate
x^2-4x+7=(x-2)^2+3 so the vertex is at (2,3)
saifoo.khan
  • saifoo.khan
http://i1.kym-cdn.com/entries/icons/original/000/009/993/tumblr_m0wb2xz9Yh1r08e3p.jpg
mathmate
  • mathmate
Good job livelaughlilz! Speed+accuracy!
mathmate
  • mathmate
I like his movies! :)
anonymous
  • anonymous
oh so the answer is 343. the lowest value of x is 2, and if you plug it in you get 7^3=343
saifoo.khan
  • saifoo.khan
Yes^ @livelaughlilz
mathmate
  • mathmate
7^2 = ???
saifoo.khan
  • saifoo.khan
@mathmate : haha, nice. My brother just love his movies. i don't. :/
mathmate
  • mathmate
Nevermind, I was out of my mind. Yes, 7^3=343
saifoo.khan
  • saifoo.khan
You were thinking about Jackie Chan. :D
KingGeorge
  • KingGeorge
As a sidenote @mathmate, you can find the x-coordinate of the vertex using the formula \[v_x=\frac{-b}{2a}\]
mathmate
  • mathmate
Thank you for the defence, even though it was a lame one! Good thinking! :)
saifoo.khan
  • saifoo.khan
I simply love this method. Satellite73 taught me this. -b/2a
anonymous
  • anonymous
to add onto @KingGeorge the y-coordinate of the vertex is -[(b^2-4ac)/(4a)]
mathmate
  • mathmate
Thank you @KingGeorge, my memory is limited and sometimes defective. But thanks for the shortcut anyway!
anonymous
  • anonymous
you can figure all that out by completing the square of y=ax^2+bx+c
anonymous
  • anonymous
and making y=ax^2+bx+c into vertex form
mathmate
  • mathmate
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.
anonymous
  • anonymous
well b^2-4ac is also the discriminant...
saifoo.khan
  • saifoo.khan
@livelaughlilz is a boss at this.
mathmate
  • mathmate
Perhaps from this time on I will remember. Practice makes perfect! :)
mathmate
  • mathmate
Actually what I do is finding it by c-(b/2a)^2, which is exactly what we do when we complete the square.
anonymous
  • anonymous
oh
anonymous
  • anonymous
i'm going to close this question now. thanks everyone!
mathmate
  • mathmate
See you all!

Looking for something else?

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