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The value of ‘a’ for which x^{3}  3x + a = 0 has two distinct roots in [0, 1] is given by
The value of ‘c’ in Lagrange’s mean value theorem for f (x) = x (x 2)^{2} in [0, 1]
For the function f (x) = x^{3}  6x^{2} + ax + b, if Roll’s theorem holds in [1, 3] with
Find Value of ‘c’ by using Rolle’s theorem for f (x) = log (x^{2} + 2)  log 3 on [1,1]
The chord joining the points where x = p and x = q on the curve y = ax^{2} + bx + c is parallel to the tangent at the point on the curve whose abscissa is
The least value of k for which the function f(x) = x^{2} + kx + 1 is a increasing function in the interval 1 < x < 2
The interval in which f (x) = x^{3}  3x^{2}  9x + 20 is strictly decreasing
The number of stationary points of f (x) = sin x in [0,2π] are
Local minimum values of the function
If the function has maximum at x =3, then the value of ‘a’ is
The point at which f (x) = (x 1)^{4} assumes local maximum or local minimum value are
The global maximum and global minimum of f (x) = 2x^{3}  9x^{2} + 12x + 6 in [0, 2]
If the percentage error in the surface area of sphere is k, then the percentage error in its volume is
If an error of is made in measuring the radius of a sphere then percentage error in its volume is
The height of a cylinder is equal to its radius. If an error of 1 % is made in its height. Then the percentage error in its volume is
The slope of the normal to the curve given by
The line is a tangent to the curve then n ∈
The points on the curve at which the tangent is perpendicular to xaxis are
The point on the curve at which the tangent drawn is
The sum of the squares of the intercepts on the axes of the tangent at any point on the curve x ^{2/3} + y^{2/3}= a^{2/3} is
If the straight line x cos α + y sinα = p touches the curve at the point (a, b) on it, then
If the curves x = y² and xy = k cut each other orthogonally then k² =
The angle between the curves y = x³ and
If the curves ay + x² = 7 and x³ = y cut orthogonally at (1, 1) then a =
A particle moves along a line is given by then the distance travelled by the particle before it first comes to rest is
A particle is moving along a line such that s = 3t^{3}  8t + 1. Find the time ‘t’ when the distance ‘S’ travelled by the particle increases.
A particle moves along a line by S = t^{3}  9t^{2} + 24t the time when its velocity decreases.
447 docs930 tests

Test: Rate of Change And Approximations Test  10 ques 
Test: Tangents And Normals Test  10 ques 
Test: Maxima Minima (Derivative) Test  10 ques 
Test: Maxima Minima (Derivative) 2 Test  10 ques 
Test: Monotonicity Test  22 ques 
447 docs930 tests

Test: Rate of Change And Approximations Test  10 ques 
Test: Tangents And Normals Test  10 ques 
Test: Maxima Minima (Derivative) Test  10 ques 
Test: Maxima Minima (Derivative) 2 Test  10 ques 
Test: Monotonicity Test  22 ques 