Advertisements
Advertisements
प्रश्न
Find the slope of the tangent to the following curves at the respective given points.
y = x4 + 2x2 – x at x = 1
उत्तर
y = x4 + 2x2 – x
Differentiating w.r.t. ‘x’
`"d"y)/("d"x = 4x3 + 4x – 1
Slope of the tangent `(("d"y)/("d"x))_((x = 1))`
= 4(1)³ + 4(1) – 1
= 4 + 4 – 1
= 7
APPEARS IN
संबंधित प्रश्न
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. 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 particle’s acceleration each time the velocity is zero
If the volume of a cube of side length x is v = x3. Find the rate of change of the volume with respect to x when x = 5 units
If the mass m(x) (in kilograms) of a thin rod of length x (in metres) is given by, m(x) = `sqrt(3x)` then what is the rate of change of mass with respect to the length when it is x = 3 and x = 27 metres
A beacon makes one revolution every 10 seconds. It is located on a ship which is anchored 5 km from a straight shoreline. How fast is the beam moving along the shoreline when it makes an angle of 45° with the shore?
A conical water tank with vertex down of 12 metres height has a radius of 5 metres at the top. If water flows into the tank at a rate 10 cubic m/min, how fast is the depth of the water increases when the water is 8 metres deep?
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 tangent and normal to the following curves at the given points on the curve
x = cos t, y = 2 sin2t at t = `pi/2`
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:
Find the point on the curve 6y = x3 + 2 at which y-coordinate changes 8 times as fast as x-coordinate is
Choose the correct alternative:
The abscissa of the point on the curve f(x) = `sqrt(8 - 2x)` at which the slope of the tangent is – 0.25?
Choose the correct alternative:
The slope of the line normal to the curve f(x) = 2 cos 4x at x = `pi/12` is