Answer

Verified

349.2k+ views

**Hint:**To check that the given function follows Rolle's Theorem or not, we will use the conditions of Rolle ’s Theorem one by one. If the given function satisfies all the conditions of Rolle’s Theorem, then the function holds the Rolle’s Theorem or not. And to check the converse of Rolle’s theorem, by using the condition of Rolle’s Theorem in reverse.

**Complete step-by-step solution:**

Since, the function is given in the question as:

$\Rightarrow f\left( x \right)=\left[ x \right]$ such that $x\in \left[ 5,9 \right]$

As we know that the greatest integer function is not a continuous function for any values belonging to $x$. We can clearly understand its diagram.

Since, the first condition of Rolle’s Theorem is that the function should be a continuous function over a closed interval, is not fulfilled by the given greatest integer function. So, we can say that the given greatest integer function does not satisfy the first condition of theorem, there is no need to proceed further to check another conditions of Rolle’s theorem to verify the function $f\left( x \right)=\left[ x \right]$ for$x\in \left[ 5,9 \right]$.

Since, the given function does not satisfy Rolle's Theorem. So, no need to check the converse of Rolle’s Theorem also.

Hence, the given function does not follow Rolle's Theorem.

**Note:**Here are the conditions of the Rolle’s Theorem as:

1. Function should be continuous on a closed interval.

2. Function should be differentiable on an open interval.

3. If $f\left( a \right)=f\left( b \right)$, there exists some $c$ belonging to the interval such that $f'\left( c \right)=0$.

If the function follows the first condition then go for second and third conditions.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Guru Purnima speech in English in 100 words class 7 english CBSE

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Select the word that is correctly spelled a Twelveth class 10 english CBSE