Home
Class 12
MATHS
Let f(x)={:{(max{t^(3)-t^(2)+t+1,0letlex...

Let `f(x)={:{(max{t^(3)-t^(2)+t+1,0letlex}",",0lexle1),(min{3-t,1lttlex}",",1ltxle2):}` The function `f(x),AAx in [0,2]` is

A

continuos and diifferentiable

B

continuos but non differentiable

C

discontinuos and not differentiable

D

none of the above

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise EXAMPLE|6 Videos

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise Exercise For Session 1|7 Videos

  • MATRICES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|49 Videos

  • PAIR OF STRAIGHT LINES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

Similar Questions

Explore conceptually related problems

Let f(x) = x^(3) - x^(2) + x + 1 and g(x) = {{:(max f(t)",", 0 le t le x,"for",0 le x le 1),(3-x",",1 lt x le 2,,):} Then, g(x) in [0, 2] is

Let f(x)=x^(3)-x^(2)+x+1 and g(x)={("max "f(t) 0letlex 0lexle1),(3-x 1ltxle2):} then

If f(x)={(x,,,0lexle1),(2-x,,,1ltxle2):} then point of discontinuity fo f(f(x)) is [0,2] is,

Let f(x)={:{(x^(2)+4x",",-3lexle0),(-sinx",",0ltxle(pi)/(2)),(-cosx-1",",(pi)/(2)ltxlepi):} then

If f(x)={{:(x",",0lexle1),(2-e^(x-1)",",1ltxle2),(x-e",",2ltxle3):} and g'(x)=f(x), x in [1,3] , then

Let F(x)=int_(0)^(x)(t-1)(t-2)^(2)dt

Let f(x)=f_(1)(x)-2f_(2)(x), where f_(1)(x)={{:(min{x^(2),|x|}",",|x|le1),(max{x^(2),|x|}",",|x|gt1):} "and "f_(2)(x)={{:(min {x^(2),|x|}",",|x|gt1),(max{x^(2),|x|}",",|x|le1):} "and let "g(x)={{:(min{f(t),-3letlex,-3lexlt0}),(max{f(t),0letltx,0lexle3}):} The graph of y=g(x) in its domain is broken at

Let F(x)=int_(0)^(x)(t-1)(t-2)^(2)dt, then

ARIHANT MATHS-MONOTONICITY MAXIMA AND MINIMA-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let f(x)={:{(max{t^(3)-t^(2)+t+1,0letlex}",",0lexle1),(min{3-t,1lttlex...

    Text Solution

    |

  2. The least value of alpha in R for which 4alphax^(2)+(1)/(x)ge1, for al...

    Text Solution

    |

  3. The number of points in (-oo,oo) for which x^(2)-xsinx-cosx=0, is

    Text Solution

    |

  4. Let f : R ->(0,oo) and g : R -> R be twice differentiable functions...

    Text Solution

    |

  5. Let f:(0,oo) in R be given f(x)=overset(x)underset(1//x)int e^-(t+(1...

    Text Solution

    |

  6. The fuction f(x)=2|x|+|x+2|-||x+2|-2|x|} has a local minimum or a loca...

    Text Solution

    |

  7. A rectagular sheet of fixed permeter with sides having thir lengths in...

    Text Solution

    |

  8. A vertical line passing through the point (h, 0) intersects the ellips...

    Text Solution

    |

  9. Let f,g and h be real-valued functions defined on the interval [0,1] b...

    Text Solution

    |

  10. e total number of local maxima and local minima of the function f(x) =...

    Text Solution

    |

  11. If the function g:(-oo,oo)->(-pi/2,pi/2) is given by g(u)=2tan^-1(e^u)...

    Text Solution

    |

  12. The second degree polynomial f(x), satisfying f(0)=o, f(1)=1,f'(x)gt...

    Text Solution

    |

  13. If f(x)=x^(3)+bx^(2)+cx+dand 0 ltb^(2)ltc, then in (-oo,oo)

    Text Solution

    |

  14. If f(x)=x^(2)+2bx+2c^(2)and g(x)=-x^(2)-2cx+b^(2), such that minf(x)gt...

    Text Solution

    |

  15. The length of a longest interval in which the function 3sinx-4sin^(3...

    Text Solution

    |

  16. If f(x)=e^(1-x) then f(x) is

    Text Solution

    |

  17. The maximum value of (cosalpha(1))-(cos alpha(2))...(cosalpha(n)), u...

    Text Solution

    |

  18. If f(x) = {{:(e ^(x),,"," 0 le x lt 1 ,, ""), (2- e^(x - 1),,"," 1 lt ...

    Text Solution

    |

  19. If f(x) is a cubic polynomil which as local maximum at x=-1 . If f(2)=...

    Text Solution

    |

  20. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

    Text Solution

    |

  21. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

    Text Solution

    |