Home
Class 12
MATHS
Show that for alt=1,f(x)=sqrt(3) si nx-...

Show that for `alt=1,f(x)=sqrt(3)` `si nx-cosx-2a x+b` is decreasing on `Rdot`

Text Solution

AI Generated Solution

To show that the function \( f(x) = \sin x - \cos x - 2ax + b \) is decreasing on \( \mathbb{R} \) for \( a \geq 1 \), we need to analyze the derivative \( f'(x) \). ### Step 1: Find the derivative of \( f(x) \) The function is given as: \[ f(x) = \sin x - \cos x - 2ax + b \] ...
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    NCERT EXEMPLAR ENGLISH|Exercise Long answer types questions|10 Videos

  • APPLICATION OF DERIVATIVES

    NCERT EXEMPLAR ENGLISH|Exercise OBJECTIVE TYPES QUESTIONS|25 Videos

  • APPLICATION OF INTEGRALS

    NCERT EXEMPLAR ENGLISH|Exercise Objective Type Questions|22 Videos

Similar Questions

Explore conceptually related problems

Show that for a >=1,f(x)=sqrt(3)sinx-cosx-2a x+b is decreasing on Rdot

Show that for ageq1,\ \ f(x)=sqrt(3)sinx-cosx-2a x+b is decreasing on R .

Find the value of a in order that f(x)=sqrt(3)sinx-cosx-2a x+b decreases for all real values of xdot

Find the value of a in order that f(x)=sqrt(3)sinx-cosx-2a x+b decreases for all real values of xdot

Show that the function f(x)=cot^(-1)(sinx+cosx) is decreasing on (0,\ pi//4) and increasing on (pi//4,\ pi//2) .

Show that f(x)=tan^(-1)(sinx+cosx) is decreasing function on the interval (pi/4,pi/2)dot

Show that f(x)=tan^(-1)(sinx+cosx) is a decreasing function on the interval on (pi//4,\ pi//2) .

Show that f(x)=tan^(-1)x-x is decreasing function on Rdot

Show that f(x)=tan^(-1)x-x is decreasing function on Rdot

Show that f(x)=e^(2x) is increasing on Rdot