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Question
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?
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Solution
Slope of curve = `"dy"/'dx"` = 5 – 6x2
⇒ `"d"/"dt" ("dy"/"dx") = -12x * "dx"/"dt"`
= –12 . (3) . (2)
= –72 units/sec.
Thus, slope of curve is decreasing at the rate of 72 units/sec when x is increasing at the rate of 2 units/sec.
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