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Question
For the curve y = 5x – 2x3, if x increases at the rate of 2 units/sec, then find the rate of change of the slope of the curve when x = 3
Solution
The given curve is y = 5x – 2x3 and `dx/dt = 2` units/sec
y = 5x – 2x3
Differentiating both sides w.r.t x, we get
Slope of the curve = `dy/dx = 5 - 6x^2`
Differentiating both sides w.r.t t, we get
`=> d/dt (dy/dx) = 0 - 12x dx/dt`
`=> d/dt (dy/dx)_(x = 3) = 0 - 12 xx 3 xx2 = -72 "units/sec"`
Thus, the slope of the curve is decreasing at the rate of 72 units/sec when x = 3
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