The three options that a developer can use to detect if a value is NaN are:

B. Number.isNaN(value)
D. value !== value
E. Object.is(value, NaN)

Explanation:

A. value === Number.NaN: This comparison will not work for detecting NaN. In JavaScript, NaN is not equal to any other value, including itself, so this condition will be false for any value, including NaN.

B. Number.isNaN(value): This is the correct method to detect NaN in JavaScript. It returns true if the provided value is NaN and false otherwise.

C. value == NaN: The equality comparison with NaN will not work correctly because NaN is considered unequal to any value, including itself. Therefore, this condition will not reliably detect NaN.

D. value !== value: This is another way to detect NaN. In JavaScript, NaN is the only value that is not equal to itself. So, this condition will be true if value is NaN and false otherwise.

E. Object.is(value, NaN): This is also a correct way to detect NaN. Object.is() behaves similarly to the strict equality (===) operator, but it returns true when comparing NaN to NaN.

So, the three correct options are B, D, and E....

B. Number.isNaN(value)
D. value !== value
E. Object.is(value, NaN)

These options correctly handle the NaN value detection:

B. The Number.isNaN() method is specifically designed to check if a value is NaN.

D. NaN is the only value in JavaScript that is not equal to itself. So, checking if value !== value will return true if the value is NaN.

E. The Object.is() method can be used to compare a value with NaN since it performs a strict equality comparison. Object.is(value, NaN) will return true if the value is NaN.