Given: equation of curve y = 7x – x³ and x increases at the rate of 4 units per second.

To find how fast is the slope of the curve changing when x = 2

Equation of curve is y = 7x – x³

Differentiating the above equation with respect to x, we get slope of the curve

Let m be the slope of the given curve then the above equation becomes,

m = 7 - 3x²………(ii)

And it is given x increases at the rate of 4 units per second, so

Now differentiating the equation of slope i.e., equation(ii) we get

[by substituting the value of from equation (iii)]

When x = 2, equation(iv) becomes,

Hence the slope of the curve is changing at the rate of - 48 units/sec when x = 2