Description

This mock test of Test: Mean Value Theorem for JEE helps you for every JEE entrance exam.
This contains 5 Multiple Choice Questions for JEE Test: Mean Value Theorem (mcq) to study with solutions a complete question bank.
The solved questions answers in this Test: Mean Value Theorem quiz give you a good mix of easy questions and tough questions. JEE
students definitely take this Test: Mean Value Theorem exercise for a better result in the exam. You can find other Test: Mean Value Theorem extra questions,
long questions & short questions for JEE on EduRev as well by searching above.

QUESTION: 1

Geometrically the Mean Value theorem ensures that there is at least one point on the curve f(x) , whose abscissa lies in (a, b) at which the tangent is

Solution:

GMVT states that for a given arc between two endpoints, there is at least one point at which the tangent to the arc is parallel to the secant through its endpoints.

QUESTION: 2

When Rolle’s Theorem is verified for f(x) on [a, b] then there exists c such that

Solution:

Answer is

B) c ∈ (a, b) such that f'(c) = 0.

Statement for Rolle’s Theorem :

Suppose that a function f(x) is continuous on the closed interval [a,b] and differentiable on the open interval (a,b). Then if f(a)=f(b), then there exists at least one point c in the open interval (a,b) for which f′(c)=0.

QUESTION: 3

If the function f (x) = x^{2}– 8x + 12 satisfies the condition of Rolle’s Theorem on (2, 6), find the value of c such that f ‘(c) = 0

Solution:

f (x) = x^{2} - 8x + 12

Function satisfies the condition of Rolle's theorem for (2,6).

We need to find c for which f’(c) = 0

f’(x) = 2x – 8

f’(c) = 2c – 8 = 0

c = 4

QUESTION: 4

The value of c for which Lagrange’s theorem f(x) = |x| in the interval [-1, 1] is

Solution:

For LMVT to be valid on a function in an interval, the function should be continuous and differentiable on the interval

Here,

f(x) = |x| , Interval : [-1,1]

For h>0,

f’(0) = 1

For h<0,

f’(0) = -1

So, the LHL and RHL are unequal hence f(x) is not differentiable at x=0.

In [-1,1], there does not exist any value of c for which LMVT is valid.

QUESTION: 5

To verify Rolle’s Theorem which one is essential?

Solution:

Rolle’s Theorem:

If a real-valued function f is continuous on a proper closed interval [a, b], differentiable on the open interval (a, b), and f (a) = f (b), then there exists at least one c in the open interval (a, b) such that

f’(c) = 0

### Mean Value Theorem

Video | 06:37 min

### Mean Value Theorem

Video | 16:48 min

### Mean Value Theorem

Video | 06:37 min

### Mean Value Theorem

Doc | 1 Page

- Test: Mean Value Theorem
Test | 5 questions | 10 min

- Test: Mean Value Of Capacity Ratio
Test | 10 questions | 10 min

- Test: Arithmetic Mean
Test | 10 questions | 10 min

- Test: Mean
Test | 10 questions | 20 min

- Test: Mean Deviation
Test | 10 questions | 10 min