Find c of the Lagrange’s mean value theorem for which


Correct option is

It is clear that (x) has a definite and unique value of each

x Ïµ [1, 5].  

Thus, every point in the interval [1, 5] the value of f (x) is equal to the limit of f (x)   

So, f (x) is continuous in the interval [1, 5]  

Also,  which clearly exists for all x in open interval (1, 5)  

Hence, (x) is differentiable in (1, 5)  

So, there must be a value c Ïµ (1, 5) such that,  





Clearly  such that Lagrange’s Theorem is satisfied.



Find the equation of tangent to the curve y2 = 4ax at (at2, 2at).


Find the sum of the intercepts on the axes of coordinates by any tangent to the curve,  



The tangent represented by the graph of the function y = (x) at the point with abscissa x = 1 form an angle π/6 and at the point x = 2 an angle of π/3 and at the point x = 3 an angle π/4. Then find the value of,  



Three normals are drawn from the point (c, 0) to the curve y2 = x, show that c must be greater than ½. One normal is always the x-axis. Find c for which the other normals are perpendicular to each other.


Find the acute angle between the curves y = | x2 – 1| and y = | x2 – 3 | at their points of intersection when x > 0.


If the relation between subnormal SN and subtangent ST at any point S on the curve; by2 = (x + a)3 is p(SN) = q(ST)2, then find the value of p/q. 


 in which interval


If f (x) = xα log x and f (0) = 0, then the value of ‘α’ for which Rolle’s theorem can be applied in [0, 1] is:


If abc be non-zero real numbers such that  


Then the equation ax2 + bx + c = 0 will have


Let f (x) and g (x) be differentiable for 0 ≤ x ≤ 2 such that (0) = 2, g(0) = 1 and f (2) = 8. Let there exists a real number c in [0, 2] such that f’(c) = 3g’(c) then the value of g(2) must be: