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## Question

### Solution

Correct option is

Consider the function f (x) = tan x, defined on [a, b] such that

Applying lagrange’s mean value theorem, we have

#### SIMILAR QUESTIONS

Q1

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.

Q2

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

Q3

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.

Q4

in which interval

Q5

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:

Q6

If abc be non-zero real numbers such that

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

Q7

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

Q8

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:

Q9

If f (x) = loge x and g(x) = x2 and c Ïµ (4, 5), then  is equal to:

Q10

In [0, 1] lagrange’s mean value theorem is not applicable to