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

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Manager
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If x be real, find the maximum value of the expression -2x^2 [#permalink]

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18 Mar 2005, 15:18
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Question Stats:

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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
[Reveal] Spoiler: OA

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18 Mar 2005, 16:19
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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.
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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

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Re: If x be real, find the maximum value of the expression -2x^2 [#permalink]

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05 Mar 2014, 03:35
Bunuel, can you please tell if this is a GMAT question??
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Re: If x be real, find the maximum value of the expression -2x^2 [#permalink]

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05 Mar 2014, 04:42
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 [ 18.86 KiB | Viewed 2613 times ]

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Last edited by Edvento on 05 Mar 2014, 06:52, edited 1 time in total.

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Re: If x be real, find the maximum value of the expression -2x^2 [#permalink]

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05 Mar 2014, 05:19
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

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

Hope it helps.
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Re: If x be real, find the maximum value of the expression -2x^2   [#permalink] 05 Mar 2014, 05:19
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