The given curve is \\\\(y = 3x ^4-4x\\\\). Thus, the slope of the tangent to the given curve at \\\\(x = 4\\\\) is given by, \\\\(\\displaystyle \\left[\\frac{dy}{dx}\\right]_{x=4} =\\left[12x^3-4\\right]_{x=4}\\\\)=\\\\( 12(4)^3-4=12(64)-4=764\\\\)