On the intervals [0, 1 ] the function x25 ( 1 - x ) 75 takes its maximum value at the point:
1/4
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 displacement s of a particle at time 't' is given by s = a cos ωt + b sin ωt.Acceleration at time 't' is.
ω2s
s2/ω2
ω2
-ω2s
Divide 20 into two parts such that the product of one part and the cube of the other is maximum then two parts
( 10, 10)
( 12, 8 )
( 15, 5 )
Tangents to curve y = x3 at x = -1 and x = 1 are
Parallel
Intersecting obliquely
Perpendicular to each other
The largest value of ax3 - 3x2 - 12x = 5 for -2 ≤ x ≤ 4 occurs at x =
-2
The point on the curve y2 = x, whose the tangent makes an angle of 45o with x - axis will be given by
( 1/2, 1/4 )
( 1/2, 1/2 )
( 1/4, 1/2 )
If y = a log | x | + bx2 + x has its extreme value at x = -1 and x = 2 then:
a = 2, b = -1
a = 2, b = -1/2
a = -2, b = 1/2
The tangent to a given curve is perpendicular to x-axis if
The slope of the tangent to the curve y = 16 - x2 at x = 0 is
0
2
16