Question

 

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

Solution

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.

SIMILAR QUESTIONS

Q1

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

Q2

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

                                

Q3

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,  

                                                

Q4

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.

Q5

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

Q6

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. 

Q7

 in which interval

Q8

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:

Q9

If abc be non-zero real numbers such that  

                                                                      

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

Q10

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: