Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
629 views
in Continuity and Differentiability by (51.9k points)

Verify Lagrange’s mean value theorem for the functions on the indicated intervals. Find a point ‘c’ in the indicated interval as stated by the Lagrange’s mean value theorem:

f(x) = sin x – sin 2x – x on [0, π]

1 Answer

0 votes
by (50.8k points)
selected by
 
Best answer

Given as f(x) = sin x – sin 2x – x on [0, π]

Sin x and cos x functions are continuous everywhere on (−∞, ∞) and differentiable for all arguments. Therefore both the necessary conditions of Lagrange’s mean value theorem is satisfied. So, there exist a point c ∈ (0, π) such that:

Differentiate with respect to x

For the f'(c), put the value of x = c in f'(x)

f'(c) = cos c - 2cos 2c - 1

For the f(π), put the value of x = π in f'(x)

For the f'(0), put the value of x = 0 in f'(x)

From the quadratic equation, ax2 + bx + c = 0

Thus, lagrange's mean value theorem is verified.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...