Home
Class 12
MATHS
Let f(x)=x^2+(1/x^2) and g(x)=x-1/x xin...

Let `f(x)=x^2+(1/x^2)` and `g(x)=x-1/x` `xinR-{-1,0,1}`. If `h(x)=(f(x)/g(x))` then the local minimum value of `h(x)` is: (1) 3 (2) `-3` (3) `-2sqrt(2)` (4) `2sqrt(2)`

A

3

B

`-3`

C

`-2sqrt2`

D

`2sqrt2.`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • APPLICATIONS OF DERIVATIVES

    MODERN PUBLICATION|Exercise CHAPTER TEST (1)|12 Videos

  • APPLICATIONS OF DERIVATIVES

    MODERN PUBLICATION|Exercise CHECK YOUR UNDERSTANDING|10 Videos

  • APPLICATIONS OF THE INTEGRALS

    MODERN PUBLICATION|Exercise CHAPTER TEST|12 Videos

Similar Questions

Explore conceptually related problems

Let f(x)=x^(2)+((1)/(x^(2))) and g(x)=x-(1)/(x)xi nR-{-1,0,1}. If h(x)=((f(x))/(g(x))) then the local minimum value of h(x) is: (1)3(2)-3(3)-2sqrt(2)(4)2sqrt(2)

Let f(x)=1+sqrt(x) and g(x)=(2x)/(x^(2)+1)

If f(x)=sqrt(2-x) and g(x)=sqrt(1-2x) ,then the domain of f[g(x)] is:

Let f(x)={x-1,-1<=x<0 and x^(2),0<=x<=1,g(x)=sin x and h(x)=f(|g(x)|)+[f(g(x)) Then

If int(x-1)/(x^(2)sqrt(2x^(2)-2x-1))dx=(sqrt(f(x)))/(g(x))+c then the value of f(x) and g(x) is

If f(x) = x^(2) and g(x) = (1)/(x^(3)) . Then the value of (f(x)+g(x))/(f(-x)-g(-x)) at x = 2 is

If f(x)=x^2+(1)/(x^2), g(x)=x^4+(1)/(x^4) and a+(1)/(a)=3 , then the respectively values of f(a) and g(a) are

If f(x)=cos^(-1)(x^((3)/(2))-sqrt(1-x-x^(2)+x^(3))),AA 0 le x le 1 then the minimum value of f(x) is

If (f(x))/(g(x))=h(x) where g(x)=sqrt(1-|(x^(2))/(x-1)|) and h(x)=(1)/(sqrt(|x-1|-[x])) then the domain of f(x)

MODERN PUBLICATION-APPLICATIONS OF DERIVATIVES-COMPLETITION FILE (Questions from JEE Main)
  1. Given P(x) =x^(4) +ax^(3) +bx^(2) +cx +d such that x=0 is the only re...

    Text Solution

    |

  2. The equation of the tangent to the curve y""=""x""+4/(x^2) , that is p...

    Text Solution

    |

  3. Let f: R-> R be a positive increasing function with lim(x->oo)(f(3x))/...

    Text Solution

    |

  4. Let f:""RvecR be defined by f(x)""={k-2x , if""xlt=-1 2x+3,f""x >-1} ....

    Text Solution

    |

  5. The shortest distance between line y-x=1 and curve x=y^2 is

    Text Solution

    |

  6. A spherical balloon is filled with 4500p cubic meters of helium gas...

    Text Solution

    |

  7. The real number k for which the equation, 2x^3+""3x""+""k""=""0 has tw...

    Text Solution

    |

  8. If f and g are differentiable functions in [0, 1] satisfying f(0)""=""...

    Text Solution

    |

  9. If x = -1 and x = 2 are extreme points of f(x) = alpha log|x| + beta x...

    Text Solution

    |

  10. The normal to the curve x^(2) +2xy-3y^(2)=0, at (1, 1):

    Text Solution

    |

  11. Let f(x) be a polynomial of degree four having extreme values at x=1 a...

    Text Solution

    |

  12. Consider f(x)=tan^(-1)(sqrt((1+sinx)/(1-sinx))), x in (0,pi/2)dot A n...

    Text Solution

    |

  13. The normal to the curve y(x-2)(x-3)=x+6 at the point where the curve i...

    Text Solution

    |

  14. Twenty metres of wire is available for fencing off a flower-bed in ...

    Text Solution

    |

  15. If the curves y^2=6x, 9x^2+by^2=16 intersect each other at right angle...

    Text Solution

    |

  16. Let f(x)=x^2+(1/x^2) and g(x)=x-1/x xinR-{-1,0,1}. If h(x)=(f(x)/g(x)...

    Text Solution

    |

  17. The maximum values of 3 costheta+5sin(theta-(pi)/(6)) for any real val...

    Text Solution

    |

  18. Let f(x) be an non - zero polynomial of degree 4. Extremum points of f...

    Text Solution

    |