If `y=7x-x^3` and `x` increases at the rate of `4` units per second, how fast is the slope of the curve changing when `x=2` ?

Explanation

To solve the problem, we will follow these steps:

1. **Identify the given function and rates**: We have the function \( y = 7x - x^3 \) and we know that \( \frac{dx}{dt} = 4 \) units per second.

2. **Find the slope of the curve**: The slope of the curve \( m \) is given by the derivative \( \frac{dy}{dx} \). We will differentiate \( y \) with respect to \( x \):
\[ \frac{dy}{dx} = \frac{d}{dx}(7x - x^3) = 7 - 3x^2 \]
...