Question

Find the slope of the tangent to the curve y = 3x 4 − 4x at x = 4.

Answer 1

given curve , y = 3x⁴ - 4x at x = 4

we know slope of tangent of curve = value of 1st derivative of given curve.

differentiate y with respect to x
$\frac{dy}{dx}=\frac{d(3x^4-4x)}{dx}\\\\\frac{dy}{dx}=3x^{4-1}(4) - 4x^{1-1}(1)\\\\\frac{dy}{dx}|_{x=4}=12x^3-4\\\\\frac{dy}{dx}|_{x=4}=12(4)^3-4=768 - 4 = 764$

hence, slope of tangent = 764