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10 May 2021, 07:15
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
77% (01:12) correct
23%
(02:35)
wrong
based on 163
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If \(m = 4-(4-x)^2\), what is the greatest possible value of m?
(A) -12
(B) -4
(C) 0
(D) 4
(E) 20
(A) -12
(B) -4
(C) 0
(D) 4
(E) 20
Updated on: 17 May 2021, 08:20
Originally posted by Fdambro294 on 10 May 2021, 07:38.
Last edited by Fdambro294 on 17 May 2021, 08:20, edited 1 time in total.
Last edited by Fdambro294 on 17 May 2021, 08:20, edited 1 time in total.
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(B) 4
The quick, logical analysis answer is to look at the function on the right side of the equation that is used to determine the value of M
The constant 4 is being subtracted by an (expression) squared
For any real value or X ————-> (4 - X)^2 will result in a non-negative output value - either 0 or some (+)positive value
This non-negative value is then subtracted from 4. The best we can hope for is to have the output value of (4 - x)^2 to be equal to = 0
in which case none of the positive 4 value will be “chipped away at” by the negative value
When X = 4
M = 4 - (4 - 4)^2
M = 4 - 0
MAX value of M occurs at: M = 4
You can also see this by letting M be one of the positive value answers ———> M = 20, option E
M = 20 = 4 - (4 - x)^2
16 = - [(4 - x) (4 - x) ]
16 = - [ 16 - 8x + x ^2 ]
16 = -16 + 8x - (x)^2
(x)^2 - 8x + 32 = 0
(x)^2 - 8x + 16 + 16 = 0
(x - 4)^2 + 16 = 0
(x - 4)^2 = -16
The output of any value Squared can never be a negative value
The best we can hope for is to eliminate the - (4 - x)^2 in the original equation and have M = 4
(b) 4
Edit: should be (D) 4
Not (B) 4 - wrote down the wrong answer choice to accompany the answer
Posted from my mobile device
The quick, logical analysis answer is to look at the function on the right side of the equation that is used to determine the value of M
The constant 4 is being subtracted by an (expression) squared
For any real value or X ————-> (4 - X)^2 will result in a non-negative output value - either 0 or some (+)positive value
This non-negative value is then subtracted from 4. The best we can hope for is to have the output value of (4 - x)^2 to be equal to = 0
in which case none of the positive 4 value will be “chipped away at” by the negative value
When X = 4
M = 4 - (4 - 4)^2
M = 4 - 0
MAX value of M occurs at: M = 4
You can also see this by letting M be one of the positive value answers ———> M = 20, option E
M = 20 = 4 - (4 - x)^2
16 = - [(4 - x) (4 - x) ]
16 = - [ 16 - 8x + x ^2 ]
16 = -16 + 8x - (x)^2
(x)^2 - 8x + 32 = 0
(x)^2 - 8x + 16 + 16 = 0
(x - 4)^2 + 16 = 0
(x - 4)^2 = -16
The output of any value Squared can never be a negative value
The best we can hope for is to eliminate the - (4 - x)^2 in the original equation and have M = 4
(b) 4
Edit: should be (D) 4
Not (B) 4 - wrote down the wrong answer choice to accompany the answer
Posted from my mobile device
Westfolia007
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10 May 2021, 12:09
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The above equation can be written as M = 2^2 - (4 - x)^2 { a^2 - b^2}
Therefore, M = (6-x)(x-2) { a^2 - b^2 = (a+b)(a-b) }
The value of M will be maximum when (6-x) and (x-2) are very close to each other or equal
6-x = x-2 will give x = 4
Hence the value of M is 2*2 = 4
Option D according to me
Therefore, M = (6-x)(x-2) { a^2 - b^2 = (a+b)(a-b) }
The value of M will be maximum when (6-x) and (x-2) are very close to each other or equal
6-x = x-2 will give x = 4
Hence the value of M is 2*2 = 4
Option D according to me
