Find the smallest value of this function.

[PrudensOptimus]

f(x) = x^2 - 3x + sqrt(x-3) - sqrt(x+3)

Using algebra, geometry, calculus, whatever you want, but do not use a calculator :p

Also must show work.

Very interesting math problem I saw on the web.

 

[dduardo]

what is with the 'n'. Isn't it supposed to be an x.

The function has complex roots because of the sqrt's. So want do you mean by smallest value. Smallest real number or smallest imaginary number?

 

[PrudensOptimus]

both.

 

[HallsofIvy]

Actually, neither the question by dduardo, "The function has complex roots because of the sqrt's. So want do you mean by smallest value. Smallest real number or smallest imaginary number?", nor the response by PrudensOptimus, "Both" make any sense.

In the first place, the question asked about the smallest value of the function- it didn't say anything about roots. Secondly, the complex numbers cannot be ordered so it never makes sense to ask about the "smallest" complex number.

The function f(x)= x^2 - 3x + sqrt(x-3) - sqrt(x+3)
is only defined for x>= 3 and it's pretty easy to see that it is an increasing function. The smallest value occurs at x= 3 and is
f(3)= 9- 9+ sqrt(0)- sqrt(6)= - sqrt(6).

 

[PrudensOptimus]

:) I got it right yay

it is from the restriction 4sqrt[(x-3)(x+3)].

 

[StarkyDee]

someone show me the work for this please, I am a dumb butt..