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

y = 5x – 2x³

x increases at rate of 2 units/sec which means as it is increasing hence it is positive

Slope of the curve is given by let it be denoted by m

We have to find change in slope with respect to time that is when x = 3 that is

Let us first find the slope m

Differentiate y with respect to x

Hence slope is given as

⇒ m = 5 – 6x²

Now differentiate m with respect to t

Given that

But we have to find the change at x = 3 hence put x = 3

The negative sign indicates that the slope is decreasing

Hence slope of given curve decreasing at 72 units/sec