Home
Class 12
MATHS
Find the intervals in which function f(x...

Find the intervals in which function f(x) = `sin x-cos x, 0 lt x lt 2pi ` is (i) increasing, (ii) decreasing.

Text Solution

AI Generated Solution

To find the intervals in which the function \( f(x) = \sin x - \cos x \) is increasing or decreasing on the interval \( 0 < x < 2\pi \), we will follow these steps: ### Step 1: Find the first derivative of the function The first step is to differentiate the function \( f(x) \). \[ f'(x) = \frac{d}{dx}(\sin x - \cos x) = \cos x + \sin x \] ...
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • APPLICATIONS OF DERIVATIVES

    NAGEEN PRAKASHAN|Exercise Exercise 6a|20 Videos

  • APPLICATIONS OF DERIVATIVES

    NAGEEN PRAKASHAN|Exercise Exercise 6b|11 Videos

  • APPLICATIONS OF INTEGRALS

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

Find the intervals in which the function f(x) = sin x +cos x,x in [0, 2pi] is (i) strictly increasing, (ii) strictly decreasing.

The interval in which the function f(x)=sin x+cos x in x in[0,2 pi] is

Knowledge Check

  • The function f(x) =(sin x) +[cos x], 0 lt x le pi//2

    A
    is continuous on `(0, pi//2)`
    B
    is strictly decreasing in `(0, pi//2)`
    C
    is stricitly increasing in `(0, pi//2)`
    D
    has global maximum value 2

  • Find the intervals in which f(x) = sin 3x, x in [0,pi/2] is (i) increasing, (ii) decreasing.

    A
    `f(x)` is increasing in `[0,pi/2]`
    `f(x)` is decreasing in `[pi/6,pi/2]`
    B
    `f(x)` is increasing in `[0,pi/6]`
    `f(x)` is decreasing in `[pi/4,pi/2]`
    C
    `f(x)` is increasing in `[0,pi/6]`
    `f(x)` is decreasing in `[pi/6,pi/2]`
    D
    `f(x)` is increasing in `[0,pi/6]`
    `f(x)` is decreasing in `[pi/6,pi/4]`

    • Similar Questions

    Explore conceptually related problems

    Find the intervals in which the function f given by f(x)=sin x-cos x, 0 lt x lt 2 pi is strictly increasing or strictly decreasing.

    Find the intervals in which the function f(x) = 2x^(3)-15x^(2)+36x + 6 is (i) increasing, (ii) decreasing.

    Write the interval for which the function f(x) = cos x, 0 le x le 2pi is decreasing

    Find the intervals in which the function f given f(x)=\ sin x-cosx ,\ 0lt=x\ lt=2pi,\ is strictly increasing or strictly decreasing.

    (a) Find the intervals in which the function f(x)=log(1+x)-x/(1+x) is (i) increasing, (ii) decreasing function. (b) Find the intervals in which the function f(x)= x/(log_(e) x),x gt 0 is increasing or decreasing.

    Find the interval in which function f(x)=sin x+cos x is strictly increasing or decreasing.

    Home
    Profile