NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 14:06 It is currently 25 Apr 2024, 14:06
Decision Tracker
My Rewards
New posts
New comers' posts

Close
GMAT Club Daily Prep
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

If x be real, find the maximum value of the expression -2x^2

User avatar
anirban16
Manager
Manager
Joined: 24 Jan 2005
Posts: 141
Own Kudos [?]: 60 [4]
Given Kudos: 0
Location: Boston
Send PM
If x be real, find the maximum value of the expression -2x^2 [#permalink] New post   18 Mar 2005, 15:18
2
Kudos
2
Bookmarks
00:00
A
B
C
D
E

Difficulty:

55% (hard)

Question Stats:

66% (02:06) correct 34% (02:00) wrong based on 135 sessions
Hide Show timer Statistics
If x be real, find the maximum value of the expression -2x^2 + x + 3

(A) 2.145
(B) 3.125
(C) 1.725
(D) 1.885
(E) 3.485

Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
ShowHide Answer
Official Answer
B
User avatar
kapslock
Manager
Manager
Joined: 15 Mar 2005
Posts: 202
Own Kudos [?]: 65 [1]
Given Kudos: 0
Location: Phoenix
Send PM
Re: If x be real, find the maximum value of the expression -2x^2 [#permalink] New post   18 Mar 2005, 16:19
1
Bookmarks
anirban16 wrote:
If x be real, find the maximum value of the expression -2x^2 + x + 3

(a) 2.145
(b) 3.125
(c) 1.725
(d) 1.885
(e) 3.485


(B) 3.125.

differentiate the expression to get x = 1/4.

substitute x = 1/4 in the expression to get 3.125.

There's a way to know this value is the maxima or the minima, by double differentiation and substituting the value. Can't remember precisely. Can someone please explain?

Thanks.
User avatar
banerjeea_98
Director
Director
Joined: 18 Nov 2004
Posts: 679
Own Kudos [?]: 198 [0]
Given Kudos: 0
Send PM
Re: If x be real, find the maximum value of the expression -2x^2 [#permalink] New post   18 Mar 2005, 16:28
"B"

Differentiate the eq
-4x+1 = 0
x = 1/4

-1/8+ 1/4+3 = (-1+2)/8 + 3 = 1/8 + 3 = 25/8 = 3.125
avatar
PareshGmat
SVP
SVP
Joined: 27 Dec 2012
Status:The Best Or Nothing
Posts: 1562
Own Kudos [?]: 7208 [0]
Given Kudos: 193
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Send PM
Re: If x be real, find the maximum value of the expression -2x^2 [#permalink] New post   05 Mar 2014, 03:35
Bunuel, can you please tell if this is a GMAT question??
User avatar
Edvento
Manager
Manager
Joined: 08 Apr 2012
Posts: 95
Own Kudos [?]: 227 [0]
Given Kudos: 14
Send PM
Re: If x be real, find the maximum value of the expression -2x^2 [#permalink] New post   Updated on: 05 Mar 2014, 06:52
Guys,

This is quite a tough GMAT question.

Solution:

-2x^2 + x + 3 = -( 2x^2 - 3x +2x - 3) = -{x(2x - 3) +(2x - 3)} = (x +1)(3 - 2x)

The graph of the quadratic expression is of the form shown in the figure attached. It is a symmetric graph that intersects the x axis at -1 and 3/2.

Due to it's symmetric nature, the maxima can be obtained at 1/4, the average of -1 and 3/2.

So the maxima will be obtained at x = 1/4.
Attachments

Quant_Problem.jpg
Quant_Problem.jpg [ 18.86 KiB | Viewed 4940 times ]


Originally posted by Edvento on 05 Mar 2014, 04:42.
Last edited by Edvento on 05 Mar 2014, 06:52, edited 1 time in total.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619012 [0]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re: If x be real, find the maximum value of the expression -2x^2 [#permalink] New post   05 Mar 2014, 05:19
Expert Reply
PareshGmat wrote:
Bunuel, can you please tell if this is a GMAT question??


It could be. Check:
what-is-the-minimum-value-of-the-function-y-x-2-4x-126302.html
a-quadratic-function-f-x-attains-a-max-of-3-at-x-1-the-87703.html

Also read last chapter of our book on Coordinate Geometry: math-coordinate-geometry-87652.html

Hope it helps.

Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
GMAT Club Bot
gmatclubot
Re: If x be real, find the maximum value of the expression -2x^2 [#permalink]
05 Mar 2014, 05:19
Moderators:
Bunuel
Math Expert
92915 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions