For the given curve: y = 5x – 2x3, when x increases at the rate of 2 units/sec, then how fast is the slope of curve changes when x = 3?

Dear student

Given that, y = 5x – 2x^3

Then, the slope of the curve, dy/dx = 5-6x^2

⇒d/dt [dy/dx]= -12x. dx/dt

= -12(3)(2)

= -72 units per second

Hence, the slope of the curve is decreasing at the rate of 72 units per second when x is increasing at the rate of 2 units per second.

Thanks