SaraNextGen Study App [2023-24]
Last Updated On [03-11-2023]

Let  be a non-constant thrice differentiable function defined on  such that  and . If  is the minimum number or roots of  in the interval [0, 6], then the value of  is


Question ID - 153400 :-

Let  be a non-constant thrice differentiable function defined on  such that  and . If  is the minimum number or roots of  in the interval [0, 6], then the value of  is

1 Answer
5876 Votes
3537

Answer Key : (6) -

(6)

     (1)

On differentiating (1) w.r.t. , we get

        (2)

Putting  in (2), we get

Similarly

has minimum 7 roots in [0, 6]

Now, consider a function

As  satisfy Rolle’s theorem in intervals  and  respectively

So, by Rolle’s theorem, the equation  has minimum 6 roots

Now , where

Clearly  has minimum 13 roots in [0, 6]

Hence again by Rolle’s theorem, has minimum 12 zeroes in [0, 6]



Next Question :

A right triangle is drawn in a semicircle of radius  with one of its legs along the diameter. If the maximum area of the triangle is , then the value of  is


View Topper Answer

We hope we have given the updated helpful answer / content for your query in an easily accessible format to help you in preparing adequately. We do offer free support materials, 11th maths guide 11th maths guide 12th maths guide 10th maths guide, also for all the classes books and guide to all the students who sign up for SaraNextGen. Apart from traditional textbook queries, we've got conjointly provided further high order level thinking issues, that are seemingly to be expected in boards and competitive exams. It includes conceptual queries, MCQs, Long and short answer type queries, etc. These Questions are designed to learn each student and academics by providing chapter-wise further issues focusing totally on testing conceptual information with applications. Here, we've got provided a number of the necessary ways in which within which the solutions of all the Questions will profit students of class 1 to 12. If you have any queries, drop a message to us and we will get back to you at the earliest.


SaraNextGen