Problem Solving

Find the minimum value of the following function:
f(x) = (x – 5)2 + (x – 7)2 – (x – 4)2 – (x – 8)2 + (x – 3)2 + (x – 9)2

priyankagumber wrote:Find the minimum value of the following function:
f(x) = (x – 5)2 + (x – 7)2 – (x – 4)2 – (x – 8)2 + (x – 3)2 + (x – 9)2

IMO minimum value is 4.

priyankagumber wrote:Find the minimum value of the following function:
f(x) = (x – 5)2 + (x – 7)2 – (x – 4)2 – (x – 8)2 + (x – 3)2 + (x – 9)2

pl. confirm that question is rightly typed or not?
I have doubt whether (x-5)2 is (x-5)*2 or (x-5)^2 and so on...

(x – 5)2 + (x – 7)2 – (x – 4)2 – (x – 8)2 + (x – 3)2 + (x – 9)2

Expanding the eqn

2x - 10 + 2x - 14 -2x +8 - 2x + 16 + 2x - 6 + 2x - 18

solving this we will end up with
4x - 24

A minumum value for this will depend on the value of x

x can extend upto -infinity.

I think in the question it must be square of..

priyankagumber wrote:Find the minimum value of the following function:
f(x) = (x – 5)2 + (x – 7)2 – (x – 4)2 – (x – 8)2 + (x – 3)2 + (x – 9)2

For this question to make any sense, each bracketed term should be ^2, not *2.

Please confirm and also provide the answer choices.

If all the terms are squares then minimum value of f(x) = 12.