1. Find the expression for the slope of the curve:

Given \(y = 7x - x^3\), differentiate with respect to \(x\) to find the slope \(m\):

\(m = \frac{dy}{dx} = 7 - 3x^2\)

2. Find the rate of change of the slope with respect to time:

Differentiate the slope \(m\) with respect to time \(t\):

\(\frac{dm}{dt} = \frac{d}{dt}(7 - 3x^2) = -6x \frac{dx}{dt}\)

3. Substitute the given values:

We are given that \(\frac{dx}{dt} = 2\) units/sec and \(x = 5\).

Substitute these values into the expression for \(\frac{dm}{dt}\):

\(\frac{dm}{dt} = -6(5)(2) = -60\) units/sec