Social pyschologists have found that as the discrepancy between the views of a speaker and those of an audience increases, the attitude change in the audience also increases to a point but decreases when the discrepancy becomes too large, particulary if the communicator is viewed by the audience as having low credibility.
Suppose that the degree of change can be approximated by the function D(x) = -x4 + 8x3 + 80x2, where x is the discrepancy between the views of the speaker and those of the audience, as measured by scores on a questionairre. Find th amount of discrepancy the speaker should aim for to maximize the attitude change in the audience.