Finding Max/Min involving perfect Square Quadratics

[xerocoool]

Hi,

For ex.
f(x) = 7 - (x+1)^2 - condition 1
f(x) = 24 + (2x+1)^2 - condition 2

Does the max/min value depend upon addition or subtraction of the perfect square term ? Is it the right way of identification ?

Solving condition 1 (assigning the square term to 0 )
f(x) = 7 - (x+1)^2
(x+1) = 0
x = -1

f(-1) = 7 - (-1+1)^2 = 7 => max value of f(x)

Solving condition 2 (assigning the square term to 0)
f(x) = 24 + (2x+1)^2
(2x+1) = 0
x = -1/2

f(-1/2) = 24 + (2 * (-1/2) + 1) = 24 => min value for f(x)

Thanks
Xeroo

[tommywallach]

Hey Xero,

I'm sorry, but I don't understand your question. What I can tell you is that there is no formulaic way to approach this type of question. The logic you seem to be applying looks good though. For example, the minimum of a squared term would be zero, so in the first example you give, because you're subtracting the squared term, the maximum for the function would be whatever makes the squared term zero. The minimum in that example doesn't exist, because you can subtract as large a number as you want.

But in all cases, you just have to logic it out in this way.

Hope that helps, and let me know if you were making some other point that I didn't entirely understand. : )

-t

[xerocoool]

So from such equations we can get only one value right ? either maximum or minimum depending on the nature of the equation.

[tommywallach]

Hey Xero,

Well you're still getting an infinite number of values from the function, so I still don't quite understand your question. If you're asking can there be a function that has both a maximum and a minimum (as opposed to just one), I don't know if there's a hard rule about that. I can't think of one off the top of my head, but I'd be nervous to state it as a rule.

What I can tell you is that it really doesn't matter, because if a question asks you for the range of a function, you'll have to go looking for the maximum and minimum anyway.

-t

[xerocoool]

Hi Tommy,

If you're asking can there be a function that has both a maximum and a minimum (as opposed to just one)

Yes, I meant this.

because if a question asks you for the range of a function, you'll have to go looking for the maximum and minimum anyway.

Got it. :)

Thanks
xero

[tommywallach]

Glad to help! (Hope I did!).

-t