Home
Class 12
MATHS
Consider f(x)=(x)/(x^(2)-1) Statement ...

Consider `f(x)=(x)/(x^(2)-1)`
Statement I Graph of `f(x)` is concave up for `xgt1.`
Statement II If `f(x)` is concave up then `f''(x)gt0`

A

Both statement I and Statement II are correct and Statement II is the correct explanation of Statement I

B

Both Statement I and Statement II are correct but Statement II is not the correct explanation of Statement I

C

Statement I is correct but Statement II is incorrect

D

Statement II is correct but Statement I is incorrect.

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|16 Videos
  • DIFFERENTIATION

    ARIHANT MATHS|Exercise Exercise (Subjective Type Questions)|15 Videos
  • DIFFERENTIATION

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|64 Videos
  • DIFFERENTIAL EQUATION

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|26 Videos
  • DY / DX AS A RATE MEASURER AND TANGENTS, NORMALS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

Similar Questions

Explore conceptually related problems

Consider f(x)=(x)/(x^(2)-1)and(x)=f''(x) Statement I Graph of g(x) is cancave up for xgt1 . Statement II (d^(n))/(dx^(n))f(x)=((-1)^(n)n!)/(2){(1)/((x-1)^(n+1))+(1)/((x+1)^(n+1))}n"inN

Consider the function f(x)=(.^(x+1)C_(2x-8))(.^(2x-8)C_(x+1)) Statement-1: Domain of f(x) is singleton. Statement 2: Range of f(x) is singleton.

Consider the graph of the function f(x)=x sqrt(|x|) Statement-1: The graph of y=f(x) has only one critical point Statement-2: f'(x) vanishes only at one point

Consider the function f(x)=(.^(x+1)C_(2x-8))(*^(2x-8)C_(x+1)) statement -1: Domain of f(x) is singleton.Statement -2: Range of f(x) is singleton.

Let f(x)=cos(x cos((1)/(x))) statement- -1:f(x) is discontinuous at x=0. Statement- 2: Lim -(x rarr0)f(x) does not exist.

f(x)=[(cosx,-sinx,0),(sinx,cosx,0),(0,0,1)] Statement 1: f(x) is inverse of f(-x) Statement 2: f(x).f(y) = f(x+y)

Let f(x) =(x+1)^(2) - 1, x ge -1 Statement 1: The set {x : f(x) =f^(-1)(x)}= {0,-1} Statement-2: f is a bijection.

Let f be a function defined by f(x)=(x-1)^(2)+1,(xge1) . Statement 1: The set (x:f(x)=f^(-1)(x)}={1,2} Statement 2: f is a bijection and f^(-1)(x)=1+sqrt(x-1),xge1 .

Statement I f(x) = sin x + [x] is discontinuous at x = 0. Statement II If g(x) is continuous and f(x) is discontinuous, then g(x) + f(x) will necessarily be discontinuous at x = a.

Let f(x) = sin^(-1)((2x)/(1+x^(2))) Statement I f'(2) = - 2/5 and Statement II sin^(-1)((2x)/(1 +x^(2))) = pi - 2 tan^(-1) x, AA x gt 1