Use the Rational Zero Theorem to list all possible rational zeros for the given function.
\[
f(x)=4 x^{4}-x^{3}+5 x^{2}-4 x-14
\]

Which of the following is the complete list of possible zeros of the given function?
A.
\[
\pm 1, \pm 2, \pm \frac{7}{2}, \pm \frac{1}{4}, \pm \frac{7}{4}
\]
B.
\[
\pm 1, \pm 2, \pm 7, \pm 14, \pm \frac{1}{2}, \pm \frac{7}{2}, \pm \frac{1}{4}, \pm \frac{7}{4}
\]
c.
\[
\pm 1, \pm 2, \pm 7, \pm \frac{1}{2}, \pm \frac{7}{2}
\]
D. The function has no rational zeros.

Step 1 ：Given the function \(f(x)=4 x^{4}-x^{3}+5 x^{2}-4 x-14\).

Step 2 ：The Rational Zero Theorem states that if a polynomial function has integer coefficients, then every rational zero will have the form p/q where p is a factor of the constant term and q is a factor of the leading coefficient.

Step 3 ：In this case, the constant term is -14 and the leading coefficient is 4.

Step 4 ：We need to find all the factors of -14 and 4, and then form all possible fractions p/q where p is a factor of -14 and q is a factor of 4.

Step 5 ：The factors of 14 are \(\pm 1, \pm 2, \pm 7, \pm 14\).

Step 6 ：The factors of 4 are \(\pm 1, \pm 2, \pm 4\).

Step 7 ：Forming all possible fractions p/q where p is a factor of -14 and q is a factor of 4, we get \(\pm 1, \pm 2, \pm 7, \pm 14, \pm \frac{1}{2}, \pm \frac{7}{2}, \pm \frac{1}{4}, \pm \frac{7}{4}\).

Step 8 ：\(\boxed{\text{Final Answer: The complete list of possible zeros of the given function is } \pm 1, \pm 2, \pm 7, \pm 14, \pm \frac{1}{2}, \pm \frac{7}{2}, \pm \frac{1}{4}, \pm \frac{7}{4}}\)