Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. algebra
  3. 154 mathematics proof a let x x a b be such that x

154 MATHEMATICS Proof a Let x x a b be such that x x Then...

50.1K

Verified Solution

Question

Algebra

image

154 MATHEMATICS Proof a Let x x a b be such that x x Then by Mean Value Theorem Theorem 8 in Chapter 5 there exists a point c between and X x such that i e i e Thus we have Rationalised 2023 24 f x f x f c x x f x f x 0 f x f x X x Hence f is an increasing function in a b f x f x for all x x a b is increasing on R Solution Note that The proofs of part b and c are similar It is left as an exercise to the Remarks There is a more generalised theorem which states that if f x for x in an interval excluding the end points and fis continuous in the interval then fis increasing Similarly if f x 0 for x in an interval excluding the end points and fis continuous in the interval then fis decreasing Example 8 Show that the function f given by f x 3x 6x 4 as f c 0 given 3 x 2x 1 1 t to be po hod 3 x 1 1 0 in every interval of R Therefore the function fis increasing on R Example 9 Prove that the function given by f x cos x is a decreasing in 0 b increasing in 1 2 and c neither increasing nor decreasing in 0 2

Answer & Explanation Solved by verified expert
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Finance
1.2K views

Tocserp is considering the purchase of a new machine that will produce widgets. The widget maker...

General Management
1.2K views

How is the (Goals, Work teams, planning) affect the implementing of a group project?

Physics
1.2K views

N An a particle experiences a force of 3 84x10 14 when its moves perpendicular...

Basic Math
1.2K views

A marble is drawn from a box containing 4 yellow 5 white and 18 blue...

Basic Math
1.2K views

A total of 443,818 students at 699 community colleges in 48 states completed the Community...

Basic Math
1.2K views

A relation contains the points (1, 2), (2, -1), (3, 0), (4, 1), and (5,-1)....

Statistics
1.2K views

The life expectancy in years for a particular brand of microwave oven is a continuous...

Accounting
1.2K views

Cullumber Innovations, Inc. produces exercise and fitness gear. Two of its newer products require a...

Accounting
1.2K views

Based on the following information: Which products should be processed further or not? Why? Give...

Accounting
1.2K views

Selected account information (in $ millions) from Target Corporations 2011 annual report follows. While the...

Accounting
1.2K views

I need help with the inventory section of the general journal. Wiset Company completes these...

Accounting
1.2K views

Organic Food Cos cash account shows a $6,700 debit balance and its bank statement shows...