6. Let $f(x)=a x-x^{3}\left(a \in \mathbf{R}, x \in\left[\frac{1}{2}, 1\right]\right)$ with its graph denoted as $C$. If any line with a slope no less than 1 intersects $C$ at most once, then the range of values for $a$ is $\qquad$
6. $a<\frac{7}{4}$.

Let $M\left(p, a p-p^{3}\right)$ and $N\left(q, a q-q^{3}\right)\left(p, q \in\left[\frac{1}{2}, 1\right]\right)$ be any two different points on the curve $C$, and the slope of the line $MN$ is $k$. According to the condition, for any $p \neq q, k<1$ always holds.

Since $k=a-\left(p^{2}+q^{2}+p q\right)$, and when $p, q \in \left[\frac{1}{2}, 1\right]$, $\frac{3}{4} \leqslant p^{2}+q^{2}+p q \leqslant 3$, thus,
$k_{\max }=a-\frac{3}{4}$.
Therefore, $a<\frac{7}{4}$.