Final answer:
The minimum degree of the function f(x) with the given conditions is 7, as it has 7 distinct real zeros and no relative extreme values.
Step-by-step explanation:
The student has asked about the minimum degree of a polynomial function f(x) given that the degree of f(x) is odd, the leading coefficient is positive, it has 7 distinct real zeros, and 0 relative extreme values. For a polynomial to have 7 real zeros, it must be at least of degree 7. However, for it to have 0 relative extremas (which are maxima or minima), it means that the polynomial cannot turn or change direction more than 7 times, which it would have already done to account for the 7 real zeros.
Therefore, the polynomial is a straight line passing through these zeros. This implies the polynomial is exactly degree 7, because if it were of a higher degree, there would have to be at least one relative extrema between some of the zeros.The question states that the degree of f(x) is odd and the leading coefficient is positive. It also mentions that there are 7 distinct real zeros and no relative extreme values. Since there are 7 distinct real zeros, the minimum degree of f(x) would be 7. This is because the degree of a polynomial function represents the highest power of x in the expression.