Home
Class 12
MATHS
If the derivative of the function f(x) ...

If the derivative of the function `f(x) ={ax^2+b , x lt -1 and bx^2 +ax+4,x leq -1` is everywhere continuous, then-

A

`a=3, b=2`

B

`a=2, b=3`

C

`a=-2, b=-3`

D

`a=-3, b=-2`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL DISTRIBUTION

    NIKITA PUBLICATION|Exercise MCQS|77 Videos
  • DEFINITE INTEGRAL

    NIKITA PUBLICATION|Exercise MULTIPLE CHOICE QUESTIONS|243 Videos

Similar Questions

Explore conceptually related problems

If the derivative of the function f(x)={{:(ax^(2)+b,xlt-1),(bx^(2)+ax+4,xge-1):} is every where continuous, then what are the values of a and b?

The function f(x)=xsqrt(ax-x^2), a lt 0

If the function f(x)= {(3ax +b", " x gt 1 ),(11 ", "x=1),(5 ax-2b", " x lt 1):} continuous at x= 1 then ( a, b) =?

If the function and the derivative of the function f(x) is everywhere continuous and is given by f(x)={:{(bx^(2)+ax+4", for " x ge -1),(ax^(2)+b", for " x lt -1):} , then

If the function f(x)={Ax-B,x<=1 and 3x,1

If function defined by f(x) ={(x-m)/(|x-m|) , x leq 0 and 2x^2+3ax+b , 0 lt x lt 1 and m^2x+b-2 , x leq 1 , is continuous and differentiable everywhere ,

If the function f(x) = {(a+bx",", x lt 1), (5",", x=1), (b-ax",", x gt 1):} is continuous, then what is the value of (a+b) ?

If the function f(x) is given by f(x)={{:(,2^(1//(x-1)),x lt 1),(,ax^(2)+bx,x ge 1):} is everywhere differentiable, then

NIKITA PUBLICATION-CONTINUITY-MULTIPLE CHOICE QUESTIONS
  1. If the function f:R to R given by f(x)={(x+a"," , "if "x le 1),(3...

    Text Solution

    |

  2. If f(x)={:{(ax^(2)-b", for " 0 le x lt1),(2", for " x=1),(x+1", for " ...

    Text Solution

    |

  3. If the derivative of the function f(x) ={ax^2+b , x lt -1 and bx^2 ...

    Text Solution

    |

  4. If f(x) is continuous at x=2, where f(x)={:{(4x-3", for " x lt 2),(kx...

    Text Solution

    |

  5. If f(x) is continuous at x=0, where f(x)={:{((1-cos 4x)/(x^(2))", for...

    Text Solution

    |

  6. If f(x) is continuous at x=0, where f(x)={:{((sin 4x)/(5x)+a", for " ...

    Text Solution

    |

  7. If f(x) = (sin pi x)/(x-1)+a, " for " x lt 1 = 2 pi , " for " x= 1 ...

    Text Solution

    |

  8. Let f(x)={{:(,sin2x,0 lt x le xpi//6),(,ax+b,pi//6 lt x lt 1):} If f(x...

    Text Solution

    |

  9. Determine the values of a , b , c for which the function f(x)={(sin(a+...

    Text Solution

    |

  10. Determine the values of a , b , c for which the function f(x)={(sin(a+...

    Text Solution

    |

  11. If f(x) is continuous on [-2, 2], where f(x)={:{((sin ax)/(x)+2", for...

    Text Solution

    |

  12. Find the values of a and b so that the function f(x)={{:(x+asqrt2...

    Text Solution

    |

  13. Let f(x) = {{:(-2 sin x,"for",-pi le x le - (pi)/(2)),(a sin x + b,"fo...

    Text Solution

    |

  14. If the function f(x) is continuous in the interval [-2, 2]. find the ...

    Text Solution

    |

  15. If f(x) is continuous in (-oo, 6), where f(x)={: {(1+sin ((pi x)/(2))...

    Text Solution

    |

  16. If f(x)={(ax+1",", x le (pi)/(2)),(sinx+b",", x gt (pi)/(2)):} is cont...

    Text Solution

    |

  17. If f(x)={:{((e^(1/x)-1)/(e^(1/x)+1)", for " x !=0),(1", for " x=0):}, ...

    Text Solution

    |

  18. If f(x) is continuous at x=0, where f(x){:{((1)/(1+e^(1/x))", for " x...

    Text Solution

    |

  19. The function f(x)=k ( k in R) at every x in R is

    Text Solution

    |

  20. The composition of two continuous functions is a continuous function.

    Text Solution

    |