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Helium
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15 Aug 2018, 05:07
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
25% (02:53) correct
75%
(01:51)
wrong
based on 8
sessions
History
Date
Time
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Not Attempted Yet
Find the maximum value of |30 + 9x - 3x2 |, where -1<= x <= 4
A) 30
B) 93/4
C) 147/4
D) 33
E) 36
A) 30
B) 93/4
C) 147/4
D) 33
E) 36
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15 Aug 2018, 06:21
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Harshgmat
Is the highlighted part a 3 digit number or is it a multiplication sign?
15 Aug 2018, 07:08
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Harshgmat
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 1630 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\(30 + 9(\frac{3}{2})- 3(\frac{3}{2})^2=30+\frac{27}{2}-\frac{27}{4}=\frac{147}{4}\)
