Home
Class 12
MATHS
If f(x)={:{(3x^2+12x-1"," -1le x le2),(3...

If `f(x)={:{(3x^2+12x-1"," -1le x le2),(37-x ","2 lt x le 3):}` then

A

f(x) is increasing in [-1,2]

B

f(x) is continuous in [-1,3]

C

f(x) is maximum at x=2

D

all of the above

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • MAXIMA AND MINIMA

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|29 Videos

  • MAXIMA AND MINIMA

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|7 Videos

  • MATHEMATICAL REASONING

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|20 Videos

  • MEASURES OF CENTRAL TENDENCY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|21 Videos

Similar Questions

Explore conceptually related problems

If f(x) = {{:( 3x ^(2) + 12 x - 1",", - 1 le x le 2), (37- x",", 2 lt x le 3):}, then

Show that the function f (x)={ {:(3x^(2) + 12 x - 1,- 1 le x le 2 ),(" "37 - x," "2 lt x le 3 ):} is continuous at x = 2

Let f(x)={{:(1+x",", 0 le x le 2),(3-x"," ,2 lt x le 3):} find (fof) (x).

If f (x)= {{:(1+x, 0 le x le 2),( 3x-2, 2 lt x le 3):}, then f (f(x)) is not differentiable at:

Consider the functions f(x)={(x+1",",x le 1),(2x+1",",1lt x le 2):} and g(x)={(x^(2)",", -1 le x lt2),(x+2",",2le x le 3):} The range of the function f(g(x)) is

The relation f is defined by f(x) ={(3x+2", "0le x le2),(x^(3)", "2 le x le 5):}. The relation g is defined by g(x) ={(3x+2", "0le x le1),(x^(3)", "1 le x le 5):} Show that f is a function and g is not a function

Let f (x)= {{:(2-x"," , -3 le x le 0),( x-2"," , 0 lt x lt 4):} Then f ^(-1) (x) is discontinous at x=

The points of discontinuity of the function f (x) = {{:(3x + 1"," ,0 le x lt2),(4x - 1"," ,2 lt x le 6),(5x + 2",", 6 lt x le 10 ):} are:

Suppose f:[-2,2] to R is defined by f(x)={{:(-1 " for " -2 le x le 0),(x-1 " for " 0 le x le 2):} , then {x in [-2,2]: x le 0 and f(|x|)=x}=

Let f(x) ={:{(x, "for", 0 le x lt1),( 3-x,"for", 1 le x le2):} Then f(x) is

OBJECTIVE RD SHARMA ENGLISH-MAXIMA AND MINIMA -Exercise
  1. The minimum value of (1+1/(sin^nalpha))(1+1/(cos^nalpha)) is

    Text Solution

    |

  2. The minimum value of (x-a)(x-b) is

    Text Solution

    |

  3. The altitude of a right circular cone of minimum volume circumscired a...

    Text Solution

    |

  4. If (x-a)^(2m) (x-b)^(2n+1), where m and n are positive integers and a...

    Text Solution

    |

  5. If (x-a)^(2m) (x-b)^(2n+1), where m and n are positive integers and a...

    Text Solution

    |

  6. In a triangleA B C ,/B=90^0 and b+a=4. The area of the triangle is ma...

    Text Solution

    |

  7. The function f(x) given by f(x)=|{:(x-1", "x+1", "2x+1),(x+1", ...

    Text Solution

    |

  8. Maximum area of a reactangle which can be inscribed in a circle of a...

    Text Solution

    |

  9. If f(x)={:{(3x^2+12x-1"," -1le x le2),(37-x ","2 lt x le 3):} then

    Text Solution

    |

  10. The perimeter of a sector is p. The area of the sector is maximum when...

    Text Solution

    |

  11. If a^(2)x^(4)b^(2)y^(4)=c^(6)(a,b,x,y,cgt0) then the maximum value of ...

    Text Solution

    |

  12. The function int(-1)^(x)t(e^t-1)(t-1)(t-2)^3(t-3)^5dt has local mini...

    Text Solution

    |

  13. Let f(x) be a function such that f'(a) ne 0 . Then , at x=a, f(x)

    Text Solution

    |

  14. Let a,b,c be positive real parameter and ax^2+ b/x^2gec, AA xepsilonR ...

    Text Solution

    |

  15. If xy=a^2 and S = b^2x + c^2y where a, b and c are constants then the ...

    Text Solution

    |

  16. Let f(x)=e^x sinx , slope of the curve y=f(x) is maximum at x=a if 'a'...

    Text Solution

    |

  17. If a gt b gt0 then maximum value of (ab(a^2-b^2)sinxcosx)/(a^2sin^2...

    Text Solution

    |

  18. The maximum value of the function f(x)=(1+x)^(0.3)/(1+x^(0.3)) in [0,1...

    Text Solution

    |

  19. If g(x)=max(y^(2)-xy)(0le yle1), then the minimum value of g(x) (for...

    Text Solution

    |

  20. If a,b,c are positive constants such that agtb then the maximum value...

    Text Solution

    |