Find the slope of the tangent to the curve $y = 3{x^4} - 4x$ at $x = 4.$

We have, $y = 3{x^4} - 4x$ …(i)

Differentiating (i) w.r.t. $x$, we get $\cfrac{{dy}}{{dx}} = 3 \cdot 4{x^3} - 4 \cdot 1 = 12{x^3} - 4$
Therefore the slope of the tangent at $x = 4$ is ${\left( {\cfrac{{dy}}{{dx}}} \right)_{x = 4}} = 12 \times {(4)^3} - 4 = 764$