Use the inner product $$\langle f,g \rangle = \int_0^1 f(x)g(x) \, dx$$ in the vector space $C^0 \lbrack 0,1\rbrack$ of continuous functions on the domain $\lbrack 0, 1 \rbrack$ to find $\langle f,g\rangle$, $\| f \|$, $\| g\|$, and the angle $\alpha_{f,g}$ between $f(x)$ and $g(x)$ for $$f(x) = -5 x^2 - 6 \ \mbox{ and } \ g(x) = -6 x + 6.$$
$\langle f,g\rangle =$ ,
$\|f\| =$ ,
$\|g\| =$ ,
$\alpha_{f,g}$ .