Question
Download Solution PDFAccording to the mean value theorem \(f'(x) = \frac{f(b)-f(a)}{b-a}\) then
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Mean Value Theorem: Let f : [a, b] → R be a continuous function on [a, b] and differentiable on (a, b). Then there exists some c in (a, b) such that
f'(c) = \(\rm\frac{[f (b) - f(a)] }{(b - a)}\)
Explanation:
Given that
\(f'(x) = \frac{f(b)-f(a)}{b-a}\)
According to the mean value theorem, f'(x) will be defined for some value a < xt < b, where f(x) is differentiable.
Hence, correct answer is a < xt < b.
Last updated on Jul 8, 2025
->UPSC NDA Application Correction Window is open from 7th July to 9th July 2025.
->UPSC had extended the UPSC NDA 2 Registration Date till 20th June 2025.
-> A total of 406 vacancies have been announced for NDA 2 Exam 2025.
->The NDA exam date 2025 has been announced. The written examination will be held on 14th September 2025.
-> The selection process for the NDA exam includes a Written Exam and SSB Interview.
-> Candidates who get successful selection under UPSC NDA will get a salary range between Rs. 15,600 to Rs. 39,100.
-> Candidates must go through the NDA previous year question paper. Attempting the NDA mock test is also essential.