Home
Class 12
MATHS
Let f(x) be real valued continuous funct...

Let `f(x)` be real valued continuous function on `R` defined as `f(x)=x^(2)e^(-|x|)` then
`f(x)` is increasing in

A

`(0,2)`

B

`(2,oo)`

C

`(-2,0)`

D

`(-oo,2)`

Text Solution

Verified by Experts

The correct Answer is:
A, D
We have
`f(x)=x^(2)e^(-|x|)={(x^(2)e^(-x),xge0),(x^(2)e^(x),xlt0):}`
`f^(')(x)={(xe^(-x)(2-x),xge0),(xe^(x)(x+2),xlt0):}`
`f(x)` is increasing in `(-oo,-2)uu(0,2)`
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Let f(X) be real valued continous funcion on R defined as f(X) = x^(2)e^(-|x|) Number of points of inflection for y = f(X) is

Let f be as real valued function defined by f(x)=x^(2)+1. Find fprime ^(^^)(2)

let f:R rarr R be a continuous function defined by f(x)=(1)/(e^(x)+2e^(-x))

The function f :R to R defined by f (x) = e ^(x) isd

Let f be a real-valued function defined by f(x) = 3x^(2) + 2x + 5 Find f(1).

If f(x) is a real valued function defined as f(x)=In(1-sin x) then graph of f(x) is

Let f:Rto R be a functino defined by f (x) = e ^(x) -e ^(-x), then f'(1)=

RESONANCE-TEST PAPERS-MATHEMATICS
  1. In a A B C ,A-=(alpha,beta),B-=(1,2),C-=(2,3), point A lies on the li...

    Text Solution

    |

  2. In a Delta ABC, A -= (alpha, beta), B -= (1, 2), C -= (2,3) and point ...

    Text Solution

    |

  3. Let f(x) be real valued continuous function on R defined as f(x)=x^(2)...

    Text Solution

    |

  4. Let f(x) be a real valued continuous function on R defined as f(x)=...

    Text Solution

    |

  5. Let all chords of parabola y^(2)=x+1 which subtends right angle at (1,...

    Text Solution

    |

  6. lim(xrarr(pi)/2)(1-sinxsin3xsin5x.sin7x)/(((pi)/2-x)^(2)) is k then k/...

    Text Solution

    |

  7. If derivative of y=|x-1|^(sinx) at x=-(pi)/2 is (1+api)^(b) then value...

    Text Solution

    |

  8. sin^(-1)(sin10) is a+bpi then |a+b| is

    Text Solution

    |

  9. f:[0,2pi]rarr[-1,1] and g:[0,2pi]rarr[-1,1] be respectively given by f...

    Text Solution

    |

  10. If solution of cot(sin^(-1)sqrt(1-x^(2)))=sin(tan^(-1)(xsqrt(6))),x!=0...

    Text Solution

    |

  11. The line 2x + y = 1 is tangent to the hyperbola x^2/a^2-y^2/b^2=1. I...

    Text Solution

    |

  12. One of the diameters of circle circumscribing the rectangle ABCD is4y=...

    Text Solution

    |

  13. Value of limit lim(xrarr0^(+))x^(x^(x)).ln(x) is

    Text Solution

    |

  14. Let A,B and C be square matrices of order 3xx3 with real elements. If ...

    Text Solution

    |

  15. If (a,b) and (c,d) are two points on the whose equation is y=mx+k, the...

    Text Solution

    |

  16. The equation (x)^(2)=[x]^(2)+2x where [x] and (x) are the integers jus...

    Text Solution

    |

  17. Let x^2+y^2+x y+1geqa(x+y)AAx ,y in R , then the number of possible i...

    Text Solution

    |

  18. Let P,Q,R and S be the feet of the perpendiculars drawn from point (1,...

    Text Solution

    |

  19. Let [.] denote G.I.F. and tge0 and S={(x,y):(x-T)^(2)+y^(2)leT^(2) whe...

    Text Solution

    |

  20. A function is defined as f(x)=lim(x->oo)[cos^(2n) x , if x<0) , ...

    Text Solution

    |