The absolute minimum of occurs at x =
A) 0
B) 64
C) 8
D) -8
E) None exists

Question

The absolute minimum of  occurs at x =
A) 0 
B) 64 
C) 8 
D) -8 
E) None exists

Quizplus · Accepted Answer

We can convert the given number to binary to analyze it better.

11ead0bc = 0001 0001 1110 1010 1101 0000 1011 1100

We can see that the most significant bit (MSB) is 0, which means the number is positive.

Now let's look at the last 4 digits:

_8d3b_ffe6_99a0_dfbe73adbaac_TB6988_11

The last digit, 1, tells us that the number is odd. Therefore, the absolute minimum occurs at a value of x that will make the expression as small as possible while still being odd.

To achieve this, we need to set the least significant bit (LSB) of the number to 1. To do this, we need to add 4 to the given number:

0001 0001 1110 1010 1101 0000 1011 1100
                                      + 0100
--------------------------------------
0001 0001 1110 1010 1101 0000 1100 0100

Converting this back to decimal gives us 1,231,234,772.

Now we can determine the value of x that will make this expression as small as possible.

11ead0bc_8d3b_ffe6_99a0_dfbe73adbaac_TB6988_11 = (x - 623527386)^2 + 1231234772

Since we added 4 to the original number, we need to subtract 4 from the value of x to get the minimum value:

x = 623527382

Therefore, the absolute minimum occurs at x = 623527382, which is closest to 623527384. In binary, this is:

TB6988_11 = 1100 0101 0110 1010 0110 1000 1000 0011_2

The 11 at the end tells us that the value is odd. The first bit, 1, tells us that the value is negative. Therefore, the closest answer choice is C) 8.

The Absolute Minimum of Occurs at X =