1. Find the slope of the tangent to the curve $y = 3 x ^4 - 4x \: \: at \: \: x \: \: = 4$

Given curve is,
$y = 3 x ^4 - 4x$
Now, the slope of the tangent at point  x =4  is given by
$\left ( \frac{dy}{dx} \right )_{x=4} = 12x^3 - 4$
$= 12(4)^3-4$
$= 12(64)-4 = 768 - 4 =764$

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