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

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Find the maximum value of |30 + 9x - 3x2 |-Algrebra-PS  [#permalink]

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New post 15 Aug 2018, 04:07
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Question Stats:

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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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Re: Find the maximum value of |30 + 9x - 3x2 |-Algrebra-PS  [#permalink]

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New post 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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Find the maximum value of |30 + 9x - 3x2 |-Algrebra-PS  [#permalink]

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New post 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
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\(30 + 9(\frac{3}{2})- 3(\frac{3}{2})^2=30+\frac{27}{2}-\frac{27}{4}=\frac{147}{4}\)
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Re: Find the maximum value of |30 + 9x - 3x2 |-Algrebra-PS  [#permalink]

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New post 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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Re: Find the maximum value of |30 + 9x - 3x2 |-Algrebra-PS  [#permalink]

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New post 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)
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Re: Find the maximum value of |30 + 9x - 3x2 |-Algrebra-PS &nbs [#permalink] 15 Aug 2018, 07:17
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