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mathmath333
 one year ago
Find the minimum value of
mathmath333
 one year ago
Find the minimum value of

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mathmath333
 one year ago
Best ResponseYou've already chosen the best response.3\(\large \color{black}{\begin{align} x1+x2+x3+\cdots \ \cdots+x75,\ \ x\in\mathbb{R}\hspace{.33em}\\~\\ \end{align}}\)

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.3absolute value is always +

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.3\[37\cdot 38 = 1406\]

perl
 one year ago
Best ResponseYou've already chosen the best response.1mathmath, I used computer software and did it by brute force. not elegantly

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.238 is the median value of integers 175

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2it works because of symmetry but we need to prove it i guess

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.3\[x  1 + \cdots + x  75\ge 75x  75\cdot 38 = 75x  38 \]Equality occurs at \(x=38\).

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.3Again, wrong method to do it. =_=

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.3The answer is correct, but it's the wrong approach.

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.3in case it was this then how we do it \(\large \color{black}{\begin{align} x+0+x1+x2+x3+\cdots \quad \cdots+x75,\ \ x\in\mathbb{R}\hspace{.33em}\\~\\ \end{align}}\)

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.3This function is continuous and also symmetric about \(38\), so that is where the minimum should occur as there is no maximum.

perl
 one year ago
Best ResponseYou've already chosen the best response.1if you take the derivative of that function it is negative for x < 38 and positive for x > 38

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.3Derivatives with absolute values?

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.3i dont know much calculus

perl
 one year ago
Best ResponseYou've already chosen the best response.1$$\Large x =\sqrt{x^2}$$

perl
 one year ago
Best ResponseYou've already chosen the best response.1This is not the optimal approach, maybe a last resort.

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.3Yeah, I think the best way to explain it is \(f(38+k) = f(38  k)\)

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.3i was asking for this edited question do i here also substitute \(38\) \(\large \color{black}{\begin{align} x0+x1+x2+x3+\cdots \quad \cdots+x75,\ \ x\in\mathbb{R}\hspace{.33em}\\~\\ \end{align}}\)

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.1we take some cases 1) suppose x=<0 then all the mods will open as negative and we'll get a big number 2) suppose x>=75 then all mods will open positive and in this case we'll get a big number 3)if 0<x<75 then some mods will open positive and some negative nd thus the negative ones and positive ones will cancel each other nd we'll get a smaller value so we take a middle value from the numbers 175 i.e (1+75)/2 = 38 then then'll u must be able to solve it

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.1yes @mathmath333 u have to put x = 38 in that equation

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.3Observe that \(f(37.5 + k) = f(37.5  k) \) so min should occur at \(37.5\)

perl
 one year ago
Best ResponseYou've already chosen the best response.1f(37.5) = 1406.5 f(38) = 1406

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.1plugging x = 38 u get the value of equation as 1406

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2Nice! just nitpicking on your latest reply OK ;p below is symmetric but the min value occurs somewhere else dw:1434029538657:dw

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.3but calculated 1406 for previous question adding \(380+(1406)  >1406\)

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.3Yeah, I saw that \(f(37) = f(38)\) and somehow came to the conclusion that it should be minimum at \(37.5\) Sorry abou thtat

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.3My intuition somehow always manages to stay one step behind me.

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.3\[f(37) = f(38)\] Scared me for a moment there. I was about to go to sleep.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2nope, looks ur intuition works perfectly in present problem!

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.3Nah, I got the \(x + x 1 + \cdots + x 74  + x 75\) problem wrong exactly because of the reason you posted.

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.3I have a neat problem about absolute values. Hold on. Gonna post it.

Pawanyadav
 one year ago
Best ResponseYou've already chosen the best response.0Mathematically can't solve this problem

perl
 one year ago
Best ResponseYou've already chosen the best response.1can you generalize the problem find the min of $$ \Large \sum_{k=0}^n  x  (a+k) $$

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.3It depends on the number of terms being odd/even. We covered both cases. In both cases, we see the median.

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.3how can i solve this with wolfram

perl
 one year ago
Best ResponseYou've already chosen the best response.1it exceeds wolframs computational abilities but the code is https://www.wolframalpha.com/input/?i=Min%5B+Sum%5BAbs%5Bx++k%5D%2C+%7Bk%2C+1%2C+75%7D%5D%5D

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.3also this is not working https://www.desmos.com/calculator/bpayybqovh

perl
 one year ago
Best ResponseYou've already chosen the best response.1using the graph you can estimate that the minimum is between 35 and 40. then plug this number into wolfram manually https://www.wolframalpha.com/input/?i=+Sum%5BAbs%5B37+k%5D%2C+%7Bk%2C+1%2C+75%7D%5D%5D%2C++Sum%5BAbs%5B38+k%5D%2C+%7Bk%2C+1%2C+75%7D%5D%5D%2C+Sum%5BAbs%5B39+k%5D%2C+%7Bk%2C+1%2C+75%7D%5D%5D

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.3wait desmos graph gave \( \Large y_{min}=1444\)

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.3so \(1406+38=1444\) haha indeed for the second problem \(y=38\) was correct @imqwerty u were correct indeed

perl
 one year ago
Best ResponseYou've already chosen the best response.1just change the code a little bit http://prntscr.com/7fqk52

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.3so parthkohli answer of 37.5 was incorrct ?

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.3i m still confused why 38 works on both cases

perl
 one year ago
Best ResponseYou've already chosen the best response.1you're talking about the other problem

perl
 one year ago
Best ResponseYou've already chosen the best response.1i caught a glimpse of it,

perl
 one year ago
Best ResponseYou've already chosen the best response.1g(x)= sum  x  k  , k=0..75 f(x) = sum  x  k  , k=1..75 agreed?

perl
 one year ago
Best ResponseYou've already chosen the best response.1g(37) = g(38) = 1444 f(38) = 1406

perl
 one year ago
Best ResponseYou've already chosen the best response.1According to my calculations g(37)=g(37.5) = g(38) there is a flat line there http://prntscr.com/7fqoum

perl
 one year ago
Best ResponseYou've already chosen the best response.1Therefore it is not wrong to say g(37.5) is the minimum. It is. So is g(37) and g(38)

perl
 one year ago
Best ResponseYou've already chosen the best response.1In the case f(x), we have corner , not a flat line, at the minimum.

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.3how can u prove \(g(37.5)=g(38)\)

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.3ok i saw that by zooming .

perl
 one year ago
Best ResponseYou've already chosen the best response.1and the other case is this http://prntscr.com/7fqqtn

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.3graph shows \(g(37\leq x\leq 38)=same\)

perl
 one year ago
Best ResponseYou've already chosen the best response.1I hope that's not too confusing :)

perl
 one year ago
Best ResponseYou've already chosen the best response.1Example: {1,2,3,4,5} < median is 3 {1,2,3,4} < median is 2.5 , the average of 2 and 3

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.3actually when the numbers are even like for 1,2,3,4, then median is \(2\leq x\leq 3\) any value of inequality of x will work

perl
 one year ago
Best ResponseYou've already chosen the best response.1I am curious did you mean to put a plus sign here or was this a different problem. http://prntscr.com/7fr0o7

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.3lol that was typo it should be this \(\large \color{black}{\begin{align} \left(\sum_{k=0}^{75}xk \right )\hspace{.33em}\\~\\ \end{align}}\)

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.0FWIW, in Python x sum of abs's 36.0 1410.0 36.5 1408.5 37.0 1407.0 37.5 1406.5 38.0 1406.0 38.5 1406.5 39.0 1407.0 39.5 1408.5 40.0 1410.0
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