374. Find the slope of the tangent line drawn to the curve $y=x^{3}$ at the point $C(-2;-8)$.
Solution. Let's find the derivative of the function $y=x^{3}$ at the point $x=-2$:

$$
y^{\prime}=\left(x^{3}\right)^{\prime}=3 x^{2} ; \quad y_{x=-2}^{\prime}=3(-2)^{2}=12
$$

![](https://cdn.mathpix.com/cropped/2024_05_22_db4d450c77c65a914ec1g-222.jpg?height=435&width=377&top_left_y=190&top_left_x=763)

Thus, the slope of the tangent line to the curve $y=x^{3}$ at the point $C(-2 ;-8)$ is 12 (Fig. 104).

Fig. 104