For the curve `y=5x-2x^3` , if `x` increases at the rate of 2 units/sec, then how fast is the slope of the curve changing when `x=3?`

Explanation

To solve the problem step by step, we will follow the given information and apply the necessary calculus concepts.

### Step 1: Identify the function and its derivative
We are given the curve \( y = 5x - 2x^3 \). To find the slope of the curve, we need to compute the derivative of \( y \) with respect to \( x \).

\[ \frac{dy}{dx} = \frac{d}{dx}(5x - 2x^3) = 5 - 6x^2 \]
...