Let and . Which of the following statements is correct?
A) and are not differentiable.
B) In , has more zeros than .
C) In , has less zeros than .
D) In , has the same number of zeros as .
E) There exists a value of such that .

Question

Let  and  . Which of the following statements is correct?
A) and are not differentiable. 
B) In , has more zeros than . 
C) In , has less zeros than . 
D) In , has the same number of zeros as . 
E) There exists a value of such that .

Quizplus · Accepted Answer

- For option A, there is no information given about differentiability of functions, so it cannot be determined.
- For option B, there is no information given about the number of zeros of the functions, so it cannot be determined.
- For option C, we can compare the last parts of the two numbers (after the second underscore). In the first number, the value of the third-last group is d926 and the value of the last group is afea4ba2e2df. In the second number, the value of the third-last group is d927 and the value of the last group is f79239ef6256. The third-last group has increased by one, so we know the two numbers differ by 16 in hexadecimal. This means that the corresponding values in binary differ in their fourth bit (2^2), which is the same as the number of zeros in the binary representation of 16. The last group in the first number ends in df, which has three trailing zeros in binary, so it has three zeros in its binary representation. The last group in the second number ends in 56, which has one trailing zero in binary, so it has one zero in its binary representation. Therefore, the first number has more zeros than the second number, and the statement is false.
- For option D, there is no information given about the number of zeros of the functions, so it cannot be determined.
- For option E, there is no information given about the relationship between the two functions, so it cannot be determined.