Home
Class 12
MATHS
Separate the intervals of concavity of t...

Separate the intervals of concavity of the following functions
(i) f(x)=`sin^(-1)x`,(ii) f(x)=x+sinx

Text Solution

AI Generated Solution

To determine the intervals of concavity for the given functions, we will follow these steps: ### (i) For the function \( f(x) = \sin^{-1}(x) \) 1. **First Derivative**: We start by finding the first derivative of the function. \[ f'(x) = \frac{1}{\sqrt{1 - x^2}} ...
Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE ENGLISH|Exercise Solved Examples|20 Videos
  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE ENGLISH|Exercise Concept Application Exercise 6.1|10 Videos
  • METHODS OF DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Single Correct Answer Type|46 Videos
  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE ENGLISH|Exercise Comprehension Type|6 Videos

Similar Questions

Explore conceptually related problems

Separate the intervals of monotonocity of the following function: (i) f(x)=3x^(4)-8x^(3)-6x^(2)+24x+7 (ii) F(x) =-sin^(3)x+3sin^(2)x+5,x "in" (-pi//2,pi//2) (iii) f(x)=(2^(x)-1)(2^(x)-2)^(2)

Find the domain of each of the following functions: f(x)=sin^(-1)x^2 (ii) f(x)=sin^(-1)x+sinx

Separate the intervals of monotonocity for the following function: (a) f(x) =-2x^(3)-9x^(2)-12x+1 (b) f(x)=x^(2)e^(-x) (c ) f(x) =sinx+cosx,x in (0,2pi) (d) f(x) =3cos^(4)x+cosx,x in (0,2 pi) (e ) f(x)=(log_(e)x)^(2)+(log_(e)x)

Separate the intervals of monotonocity for the function f(x)=x^2e^(-x)

Find the intervals of monotonicity of the following functions. (i) f(x) =-x^(3) +6x^(2)-gx-2 (ii) f(x) =x+(1)/(x+1) (iii) f(x) =x. e^(x-x^(2)) (iv) f(x) =x- cosx

Check the nature of the following function. (i) f(x)=sin x, x in R " (ii) " f(x) =sin x, x in N

Separate the intervals of monotonocity for the function f(x)=-2x^3-9x^2-12 x+1

The function f(x)=sin^(-1)(sinx) , is

Find the the domain of following functions: (i) f(x)=sqrt(x^(2)-5) (ii) sin(x^(3)-x)

Find the domain of each of the following functions: f(x)=sin^(-1)sqrt(x^2-1) (ii) f(x)=sin^(-1)x+sin^(-1)2x