We will use the Rational Root Test: 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 and q is a factor of the leading coefficient.

Possible rational zeros will be of the form (factor of 4) over (factor of 2).

The possible rational zeros greater than 1 are:

4/1 = 4

4/2 = 2

2/1 = 2

Lets plug the values for x into f(x)=2x^5-x^4+2x^3-2x^2+4x-4:

For x = 2

f(2) = 2*2^5-2^4+2*2^3-2*2^2+4*2-4

f(2) = 60

For x = 4

f(4) = 2*4^5-4^4+2*4^3-2*4^2+4*4-4

f(4) = 1900

Thus there is no rational zero greater than 1.