Advertisements
Advertisements
Question
Choose the correct alternative:
Find the point on the curve 6y = x3 + 2 at which y-coordinate changes 8 times as fast as x-coordinate is
Options
(4, 11)
(4, – 11)
(– 4, 11)
(– 4, – 11)
Solution
(4, 11)
APPEARS IN
RELATED QUESTIONS
A particle moves along a straight line in such a way that after t seconds its distance from the origin is s = 2t2 + 3t metres. Find the average velocity between t = 3 and t = 6 seconds
A particle moves along a straight line in such a way that after t seconds its distance from the origin is s = 2t2 + 3t metres. Find the instantaneous velocities at t = 3 and t = 6 seconds
A camera is accidentally knocked off an edge of a cliff 400 ft high. The camera falls a distance of s = 16t2 in t seconds. How long does the camera fall before it hits the ground?
A camera is accidentally knocked off an edge of a cliff 400 ft high. The camera falls a distance of s = 16t2 in t seconds. What is the average velocity with which the camera falls during the last 2 seconds?
A particle moves along a line according to the law s(t) = 2t3 – 9t2 + 12t – 4, where t ≥ 0. Find the total distance travelled by the particle in the first 4 seconds
A particle moves along a line according to the law s(t) = 2t3 – 9t2 + 12t – 4, where t ≥ 0. Find the particle’s acceleration each time the velocity is zero
A stone is dropped into a pond causing ripples in the form of concentric circles. The radius r of the outer ripple is increasing at a constant rate at 2 cm per second. When the radius is 5 cm find the rate of changing of the total area of the disturbed water?
Find the slope of the tangent to the following curves at the respective given points.
y = x4 + 2x2 – x at x = 1
Find the tangent and normal to the following curves at the given points on the curve
y = x2 – x4 at (1, 0)
Find the tangent and normal to the following curves at the given points on the curve
y = x4 + 2ex at (0, 2)
Find the tangent and normal to the following curves at the given points on the curve
y = x sin x at `(pi/2, pi/2)`
Find the equations of the tangents to the curve y = 1 + x3 for which the tangent is orthogonal with the line x + 12y = 12
Find the equations of the tangents to the curve y = `- (x + 1)/(x - 1)` which are parallel to the line x + 2y = 6
Find the angle between the rectangular hyperbola xy = 2 and the parabola x2 + 4y = 0
Show that the two curves x2 – y2 = r2 and xy = c2 where c, r are constants, cut orthogonally
Choose the correct alternative:
A balloon rises straight up at 10 m/s. An observer is 40 m away from the spot where the balloon left the ground. The rate of change of the balloon’s angle of elevation in radian per second when the balloon is 30 metres above the ground
Choose the correct alternative:
A stone is thrown, up vertically. The height reaches at time t seconds is given by x = 80t – 16t2. The stone reaches the maximum! height in time t seconds is given by
Choose the correct alternative:
The tangent to the curve y2 – xy + 9 = 0 is vertical when
