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Find the maximum value of |30 + 9x - 3x2 |-Algrebra-PS

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Director
Joined: 08 Jun 2013
Posts: 515
Location: India
GMAT 1: 200 Q1 V1
GPA: 3.82
WE: Engineering (Other)
Find the maximum value of |30 + 9x - 3x2 |-Algrebra-PS  [#permalink]

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15 Aug 2018, 04:07
00:00

Difficulty:

75% (hard)

Question Stats:

33% (01:26) correct 67% (01:23) wrong based on 12 sessions

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Find the maximum value of |30 + 9x - 3x2 |, where -1<= x <= 4

A) 30
B) 93/4
C) 147/4
D) 33
E) 36

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Senior Manager
Joined: 18 Jul 2018
Posts: 493
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Re: Find the maximum value of |30 + 9x - 3x2 |-Algrebra-PS  [#permalink]

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15 Aug 2018, 05:21
Harshgmat wrote:
Find the maximum value of |30 + 9x -3x2 |, where -1<= x <= 4

A) 30
B) 93/4
C) 147/4
D) 33
E) 36

Is the highlighted part a 3 digit number or is it a multiplication sign?
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Senior Manager
Joined: 18 Jun 2018
Posts: 250
Find the maximum value of |30 + 9x - 3x2 |-Algrebra-PS  [#permalink]

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15 Aug 2018, 06:08
Harshgmat wrote:
Find the maximum value of |30 + 9x - 3x2 |, where -1<= x <= 4

A) 30
B) 93/4
C) 147/4
D) 33
E) 36

OA:C

Expression $$30 + 9x - 3x^2$$ is of form $$ax^2+bx+c$$, $$a = -ve$$ means it is parabola which is opening down
Attachment:

parabola.jpg [ 49.66 KiB | Viewed 172 times ]

Its root can be found out by $$- 3x^2 + 9x + 30 = -3x^2+15x-6x + 30 = -3x(x-5) -6(x-5) = (-3x-6)(x-5)=0$$
$$x=-2,5$$

As parabola is opening down and expression $$30 + 9x - 3x^2$$ will be non negative between $$-2≤x≤5$$

We have to find the maximum value $$|30 + 9x - 3x^2 |$$ where $$-1≤x≤4$$ or maximum value of $$30 + 9x - 3x^2$$ where $$-1≤x≤4$$

Maximum value of $$30 + 9x - 3x^2$$ will be at $$-\frac{b}{2a}$$ i.e $$-\frac{9}{2*-3}=\frac{3}{2}$$

$$x =\frac{3}{2}$$ lies between $$-1≤x≤4$$, Value of Expression $$30 + 9x - 3x^2$$ at $$x =\frac{3}{2}$$ will be the answer.

i.e$$30 + 9(\frac{3}{2})- 3(\frac{3}{2})^2=30+\frac{27}{2}-\frac{27}{4}=\frac{147}{4}$$
Senior Manager
Joined: 18 Jul 2018
Posts: 493
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Re: Find the maximum value of |30 + 9x - 3x2 |-Algrebra-PS  [#permalink]

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15 Aug 2018, 06:11
Harshgmat wrote:
Find the maximum value of |30 + 9x - 3x2 |, where -1<= x <= 4

A) 30
B) 93/4
C) 147/4
D) 33
E) 36

Please edit the question and make it 3$$x^2$$
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When you want something, the whole universe conspires in helping you achieve it.

Intern
Joined: 10 Jul 2017
Posts: 25
Schools: ISB '20
Re: Find the maximum value of |30 + 9x - 3x2 |-Algrebra-PS  [#permalink]

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15 Aug 2018, 07:17
I used differentiation to find maximum value:
given 30+9x-3^2
or -3x^2 + 9x + 30 =0------ (1)
on differentiation -6x+9 = 0 => x=9/6 = 3/2
putting value of x in equation 1 we get => -3(3/2)^2 + 9(3/2) + 30 = 147/4 (answer)
Re: Find the maximum value of |30 + 9x - 3x2 |-Algrebra-PS &nbs [#permalink] 15 Aug 2018, 07:17
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