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
591 views
in Continuity and Differentiability by (28.9k points)
closed by

Let f(x) = x(x – 1)(x – 2), x ∈ [0, 2]

  1. Find f(0) and f(2)
  2. Find f'(x)
  3. Find the values of x when f'(x) = 0 verify Rolle’s theorem.

1 Answer

+1 vote
by (28.2k points)
selected by
 
Best answer

1. f(0) = 0, f(2) = 2(2 – 1)(2 – 2) = 0

2. We have, f(x) = x3 – 3x2 + 2x
⇒ f'(x) = 3x2 – 6x + 2.

3. f'(x) = 3x2 – 6x + 2 = 0

Clearly all the three conditions of Rolle’s theorem are satisfied and 1± \(\frac{1}{\sqrt{3}}\) ∈ (0, 2).

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.

...