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

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Solution

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

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