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livelaughlilz
 3 years ago
what is the minimum value of 7^(x^24x+7)
livelaughlilz
 3 years ago
what is the minimum value of 7^(x^24x+7)

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saifoo.khan
 3 years ago
Best ResponseYou've already chosen the best response.0\[\Large 7^{x^24x+7}\]Like this?

saifoo.khan
 3 years ago
Best ResponseYou've already chosen the best response.0@mathmate @UnkleRhaukus

saifoo.khan
 3 years ago
Best ResponseYou've already chosen the best response.0Minimum value should be there where dy/dx = 0.

livelaughlilz
 3 years ago
Best ResponseYou've already chosen the best response.1what do you mean by the "d"?

saifoo.khan
 3 years ago
Best ResponseYou've already chosen the best response.0In other words minimum value occurs where the derivative of the function is equal to zero.

livelaughlilz
 3 years ago
Best ResponseYou've already chosen the best response.1isn't derivatives calculus? i haven't learned that yet and i don't think we're expected to know it to solve this problem

livelaughlilz
 3 years ago
Best ResponseYou've already chosen the best response.1haha i was thinking about it and wouldn't it be one over infinity? because if x^24x+7 was negative infinity than 7^(x^24x+7) would be 1/infinity

mathmate
 3 years ago
Best ResponseYou've already chosen the best response.2Hint: 7^x is an increasing function. So if we minimize x, 7^x is also a minimum.

mathmate
 3 years ago
Best ResponseYou've already chosen the best response.2x^24x+7 cannot be at inf. It is a parabola concave upwards.!

saifoo.khan
 3 years ago
Best ResponseYou've already chosen the best response.0And are we going to try that by trial and error? @mathmate

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.1No, we need to simply find the vertex of the parabola to find the minimum value of the parabola.

mathmate
 3 years ago
Best ResponseYou've already chosen the best response.2Good point!] @livelaughlilz can you take it from here?

mathmate
 3 years ago
Best ResponseYou've already chosen the best response.2Completing the squares will do the job.

livelaughlilz
 3 years ago
Best ResponseYou've already chosen the best response.1yeah the vertex of the parabola is (2,3)

mathmate
 3 years ago
Best ResponseYou've already chosen the best response.2x^24x+7=(x2)^2+3 so the vertex is at (2,3)

saifoo.khan
 3 years ago
Best ResponseYou've already chosen the best response.0http://i1.kymcdn.com/entries/icons/original/000/009/993/tumblr_m0wb2xz9Yh1r08e3p.jpg

mathmate
 3 years ago
Best ResponseYou've already chosen the best response.2Good job livelaughlilz! Speed+accuracy!

livelaughlilz
 3 years ago
Best ResponseYou've already chosen the best response.1oh 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
 3 years ago
Best ResponseYou've already chosen the best response.0Yes^ @livelaughlilz

saifoo.khan
 3 years ago
Best ResponseYou've already chosen the best response.0@mathmate : haha, nice. My brother just love his movies. i don't. :/

mathmate
 3 years ago
Best ResponseYou've already chosen the best response.2Nevermind, I was out of my mind. Yes, 7^3=343

saifoo.khan
 3 years ago
Best ResponseYou've already chosen the best response.0You were thinking about Jackie Chan. :D

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.1As a sidenote @mathmate, you can find the xcoordinate of the vertex using the formula \[v_x=\frac{b}{2a}\]

mathmate
 3 years ago
Best ResponseYou've already chosen the best response.2Thank you for the defence, even though it was a lame one! Good thinking! :)

saifoo.khan
 3 years ago
Best ResponseYou've already chosen the best response.0I simply love this method. Satellite73 taught me this. b/2a

livelaughlilz
 3 years ago
Best ResponseYou've already chosen the best response.1to add onto @KingGeorge the ycoordinate of the vertex is [(b^24ac)/(4a)]

mathmate
 3 years ago
Best ResponseYou've already chosen the best response.2Thank you @KingGeorge, my memory is limited and sometimes defective. But thanks for the shortcut anyway!

livelaughlilz
 3 years ago
Best ResponseYou've already chosen the best response.1you can figure all that out by completing the square of y=ax^2+bx+c

livelaughlilz
 3 years ago
Best ResponseYou've already chosen the best response.1and making y=ax^2+bx+c into vertex form

mathmate
 3 years ago
Best ResponseYou've already chosen the best response.2Actually 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^24ac)/(4a)] part.

livelaughlilz
 3 years ago
Best ResponseYou've already chosen the best response.1well b^24ac is also the discriminant...

saifoo.khan
 3 years ago
Best ResponseYou've already chosen the best response.0@livelaughlilz is a boss at this.

mathmate
 3 years ago
Best ResponseYou've already chosen the best response.2Perhaps from this time on I will remember. Practice makes perfect! :)

mathmate
 3 years ago
Best ResponseYou've already chosen the best response.2Actually what I do is finding it by c(b/2a)^2, which is exactly what we do when we complete the square.

livelaughlilz
 3 years ago
Best ResponseYou've already chosen the best response.1i'm going to close this question now. thanks everyone!
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