# Find the slope of the tangent to the curve $y = 3x^4 – 4x \; at\; x = 4.$

$\begin{array}{1 1} 764 \\ -764 \\ 765 \\ -765 \end{array}$

Toolbox:
• If $y=f(x)$ then $\large\frac{dy}{dx}$=slope of the tangent to $y=f(x)$ at point $P$.
Step 1:
Given $y=3x^4-4x$
Slope of the tangent to the given at $x=4$ is given by,
$\large\frac{dy}{dx}$$=12x^3-4 Step 2: The slope at the given point x=4 is \large\frac{dy}{dx}_{(x=4)}$$=12(4)^3-4$
$\qquad\;\;\;\;=12(64)-4$
$\qquad\;\;\;\;=764$