Answer
The amount of discrepancy the speaker should aim for is $x=10$.
Work Step by Step
The degree of attitude change is given by, $D(x)=-x^4+8x^3+80x^2$, where $x$ is the discrepancy between the views of the speaker and audience (in scores).
We find the critical points by equating the first derivative to 0.
$D'(x)=-4x^3+24x^2+160x=0$
$x=0, x=10, x=-4$
The score of discrepancy cannot be negative or zero so $x=-4, x=0$ are rejected.
$D'(9)=468>0$ and $D'(11)=-660<0$
Since the sign of $D'(x)$ changes from $+$ to $-$ about $x=10$, $D(x)$ is maximum at $x=10$.
