﻿ Let f (x) and g (x) be differentiable for 0 ≤ x ≤ 2 such that f (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: : Kaysons Education

# Let f (x) And g (x) Be Differentiable For 0 ≤ x ≤ 2 Such That f (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:

#### Video lectures

Access over 500+ hours of video lectures 24*7, covering complete syllabus for JEE preparation.

#### Online Support

Practice over 30000+ questions starting from basic level to JEE advance level.

#### National Mock Tests

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

#### Organized Learning

Proper planning to complete syllabus is the key to get a decent rank in JEE.

#### Test Series/Daily assignments

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

## Question

### Solution

Correct option is

3

As (x) and g(x) are continuous and differentiable in [0, 2], then there exists at least one value ‘c’ such that

#### SIMILAR QUESTIONS

Q1

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

Q2

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,

Q3

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.

Q4

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

Q5

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.

Q6

in which interval

Q7

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:

Q8

If abc be non-zero real numbers such that

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

Q9

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

Q10

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