Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Explain solution RD Sharma class 12 chapter Increasing and Decreasing Functions exercise 16.2 question 37 maths

Explain solution RD Sharma class 12 chapter Increasing and Decreasing Functions exercise 16.2 question 37 maths

Answers (1)

Answer:

 f(x) is an increasing function on R or all the value of a

Given:

 f(x)=x+cos\: x -a

To prove:

We have to show that f(x) is an increasing function on R or all the value of a.

Hint:

For f(x) to be increasing function we must have f’(x) > 0.

Solution:

Here we have

f(x)=x+cos\: x -a

On differentiating both sides w.r.t x we get

\begin{aligned} &\Rightarrow f^{\prime}(x)=\frac{d}{d x}(x+\cos x-a) \\ &\Rightarrow f^{\prime}(x)=1-\sin x,\left[\frac{d}{d x}(\text { constant })=0\right] \\ &\text { Since }-1 \leq \sin x \leq 1 \end{aligned}

Then we have,

\begin{aligned} &1-\sin x \geq 0 \text { for all value of } x\\ &\operatorname{So}f^{\prime}(x) \geq 0 \text { forall } x \in R \end{aligned}

Hence the function is increasing on Rf or all value of a.

Posted by

Gurleen Kaur

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Board exams twice a year from 2025, no plan for semesters: MoE
anam-khan

CBSE Class 12 board exams 2025 to have 50% competency-based questions; no change in 10th
anam-khan

CBSE Class 12 board exams 2024 over; expected result date, trends of last 10 years

Latest Question