Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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]

Show Tags

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]

Show Tags

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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

I suppose you could solve by looking at the answer choices. If the answer is going to be correct for absolutely every value of b, it certainly must be correct when b=1. So we can let b=1 and just plug each answer choice into

x^2 + 2x + 4

to see which gives us the least value of this function. Notice answer A is completely undefined (we get a negative under the root), so cannot possibly be right. If we plug in -2 or 0, the value of the function is 4 in both cases. If we plug in answer D, which is -b^2 = -1, the function's value is 3, which is the smallest value so far. Finally if we plug in answer E, which would be equal to b - 4 = 1 - 4 = -3, the function's value is 6. So the correct answer is -b^2.

But if the GMAT were to ask a question like this, there would always be a way to correctly solve it 'from start to finish', without looking at the answer choices. And I don't see a way to do that here using normal GMAT math. I've never once needed to 'complete the square' in any official GMAT question I've ever solved, nor have I ever needed the quadratic formula, or needed to know how to find the minimum value of a general parabola. I've solved probably close to 10,000 official questions by now, so those techniques just aren't ever required on the test. This question is one that would normally be answered using calculus anyway (and is quite easy if you know calculus), so it's a question I'd bet GMAC would consider unfair, because people with certain educational backgrounds would have a big advantage answering it, and the GMAT is not supposed to be a test of whether you've ever taken a calculus class. It's a test of how well you can reason using only the most elementary facts of mathematics.

So unless I'm not seeing a solution here that uses normal GMAT math, there's really no reason to worry about this question.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

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

Show Tags

17 Jun 2016, 09:25

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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Its been long time coming. I have always been passionate about poetry. It’s my way of expressing my feelings and emotions. And i feel a person can convey...

Written by Scottish historian Niall Ferguson , the book is subtitled “A Financial History of the World”. There is also a long documentary of the same name that the...

Post-MBA I became very intrigued by how senior leaders navigated their career progression. It was also at this time that I realized I learned nothing about this during my...