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
835 views
in Continuity and Differentiability by (29.1k points)
closed by

Find the set of values of a’a’ for which f(x) = x + cos x + ax + b is increasing on R.

1 Answer

+1 vote
by (28.7k points)
selected by
 
Best answer

f(x) = x + Cos x + ax + b

f’(x) = 1 – Sin x + a + 0

f’(x) = 1 – Sin x + a

For, f(x) to be increasing, it must have

f’(x) > 0

\(\therefore\) 1 – Sin x + a > 0

1 > Sin x - a

Sin x < a + 1

\(\because\) the maximum value of Sin x is 1.

Also, 1 < a + 1

a > 0

\(\therefore\) a ∈ (0, ∞)

Hence the required set of values is a ∈ (0, ∞).

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

...