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The least value of f(x) when \((\frac{x}{b}+b)^2=0\), so when \(\frac{x}{b}+b=0\) or when \(x=-b^2\).

Answer: D.

Bunuel,

Thanks for the quick reply as always!

I still fail to see the (incomplete) square that should have triggered something in me to come up with b^2-b^2. Was the trigger the x^2/b^2? The rest is clear.

Re: If f(x)=x^2/b^2 + 2x + 4, then for each non-zero value of b [#permalink]
02 Sep 2013, 23:43

1

This post received KUDOS

In this question, we can see that the coefficient of x^2 is always positive, therefore the equation is a parabola facing upwards in a coordinate plane. In a parabola facing upwards there is only minima (no maxima) which is equal to (-coeff of x/2coeff of x^2), in this case -b^2. Hence the answer, D.

Some basic knowledge about coordinate geometry makes such questions cake walk. The GMAT Club Math Book deals with such basics appropriately.

Re: If f(x)=x^2/b^2 + 2x + 4, then for each non-zero value of b [#permalink]
02 Nov 2014, 22:36

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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