Maximum slope of a sine wave
The maximum slope for a sine wave that has no offset and an ampliutde \$A_0\$ occurs exactly during the zero crossings. Its value is simply \$A_0 \omega\$

The derivation is 
$$
\frac{d}{dt} A_0 \sin (\omega t) = A_0 \omega \cos(\omega t)
$$
which gives the slope of the sine wave.

The maximum of the cosine is 1. Therefore the maximum is \$A_0 \omega\$.
$$
\max \left\{ A_0 \omega \cos(\omega t) \right\}= A_0 \omega 
$$
The results makes sense, since intuitively the slope has to increase with the amplitude as well as the frequency.