Question

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

Answer 1

given curve , y =3x⁴ - 4x
differentiate y with respect to x ,
$\bf{\frac{dy}{dx}=3.4x^{4-1}-4.1x^{1-1}}\\\\=\bf{12x^3-4}$

we know, slope of tangent of curve y = f(x) at a point (a,b) is 1st order derivatives at that given point. e.g., $\textbf{slope of tangent}=\frac{dy}{dx}|_{(a,b)}$

hence, slope of tangent = $\bf{\frac{dy}{dx}|_{x=4}=12(4)^3-4}$
= 12(64) - 4 = 768 - 4 = 764

Answer 2

Answer:

Step-by-step explanation:

Hope you understood