The length x of a rectangle is decreasing at the rate of 3cm/min and width y is increasing at the rate of 2cm / min.When x = 10 cm and y = 6 cm,find the rate of change of the area of the rectangle is
-2
2
4
-4
For the curve x = t2 -1, y = t2 -t, the tangent line is perpendicular to x axis where:
t = 0
The radius of a circle is increasing at the rate of 0.1 cm/sec. When r = 5 cm, the rate of change of area is
π cm2/sec
0.1 cm/sec
5 π cm2/sec
2π cm2/sec
If u = x2y + y2z + z2x then ux + uy + uz =
x + y + z
2 (x + y + z)
3(x2y + y2z + z2x)
(x + y + z)2
The curve y - exy + x = 0 has a vertical tangent at the point
( 1, 1 )
At no point
( 0, 1 )
( 1, 0 )
If f (x) = x2 + ax + 1 is strictly increasing on ( 1, 2 ), then the least value of a is
1
-1
The rate of change of the area of a circle w.r.t its radius r when r = 3 is
3 π cm2/sec
6 π cm2 sec
π cm2 sec
-6 π cm2/sec
At what point the slope of the tangent to the curve x2 + y2 - 2x - 3 = 0 is zero
( 3, 0 ), ( -1, 0 )
( 3, 0 ), ( 1, 2 )
( -1, 0 ), ( 1, 2 )
( 1, 2 ), ( 1, -2 )
A man is walking at the rate of 8 kmph towards the foot of a tower 60 metres high.The rate at which he is approaching the top when he is 80 metres from the foot of the tower is.
6.4 kmph
32/3 kmph
6 kmph
None of these
The normal at the point ( 1, 1 ) to the curve 2y =3 -x2 is:
x + y = 0
x + y + 1 = 0
x - y + 1 = 0
x -y = 0
