UPSC NDA Math Model Paper 5

Given that, y=2x−x2 and

dx

dt

=3 units/sec
Then, the slope of the curve,

dy

dx

=2−2x=m
⇒

dm

dt

=0−2×

dx

dt

= -2(3)
= -6 units per second
Hence, the slope of the curve is decreasing at the rate of 6 units per second when x is increasing at the rate of 3 units per second.
Hence, option (3) is correct.