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=2,b=3`

B

`a=3,b=2`

C

`a=-2,b=-3`

D

`a=-3,b=-2`

Text Solution

Verified by Experts

The correct Answer is:
A
Derivative of `f(x)={{:(ax^(2)+b,xlt-1),(bx^(2)+ax+a,xge-1):}`
is `f(x)={{:(2ax,xlt-1),(2bx+a,xge-1):}`
If f'(x) is contnuons everywhere then it is also continuous at x=-1
`f'(x)|_(x=-1)=-2a=-2b+a`
or, 3a=2b" "…..(i)
From the given choice a=2,b=3 satisfied this equation.
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATION

    NDA PREVIOUS YEARS|Exercise MCQs|119 Videos

  • HEIGHT & DISTANCE

    NDA PREVIOUS YEARS|Exercise Math|45 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

NDA PREVIOUS YEARS-FUNCTIONS, LIMIT, CONTINUITY AND DIFFERENTIABILITY-MCQs
  1. If f(x)=(x+1)^(cotx) is continuous at x=0, then what is f(0) equal to?

    Text Solution

    |

  2. What is the value of lim(xtooo) ((x-2)/(x+2))^(x+2) = ?

    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 differentiable everywhere, then which one of the following ...

    Text Solution

    |

  5. Consider the cubic equation x^3 + ax^2 + bx + c = 0, where a, b, c are...

    Text Solution

    |

  6. If (x-a)/(b+c)+(x-b)/(c+a)+(x-c)/(a+b)=3 then value of x is

    Text Solution

    |

  7. If -x^(2)+3x+4gt0, then which one of the following is correct?

    Text Solution

    |

  8. Given f(x)=x+(1)/(x), then what is f^(2)(x) equal ot ?

    Text Solution

    |

  9. If f(x)={{:(1,x" is a rational number"),(0",","x is an irrational numb...

    Text Solution

    |

  10. A function f is defined as follows f(x)=x^(p)cos((1)/(x)),xne0 f(0...

    Text Solution

    |

  11. What is the value of lim(xto0) (sinx)/(x)?

    Text Solution

    |

  12. What is lim(xto0)(a^(x)-b^(x))/(x)?

    Text Solution

    |

  13. Let f(x)={{:(3x-4",",0lexle2),(2x+l",",2ltxle9):} If is continuous a...

    Text Solution

    |

  14. If f(x)=xandg(x)=|x|, then what is (f+g)(x) equal to ?

    Text Solution

    |

  15. If g(x)=sinx,x""inRandf(x)=(1)/(sinx),x"in(0,(pi)/(2)) what is (gof)(x...

    Text Solution

    |

  16. Let f:RtoR be defined as f(x)=sin(|x|) Which one of the following is...

    Text Solution

    |

  17. What is the inverse of the function y=5^(logx)?

    Text Solution

    |

  18. Assertion (A) : If f(x)=logx," then "f(x)gt0" for all "xgt0. Reaosn ...

    Text Solution

    |

  19. Assertion (A) : f(x) =xsin ((1)/(x)) is differentiable at x=0 Reason...

    Text Solution

    |

  20. If f(x)=log|x|,xne0, then what is f'(x) equal to ?

    Text Solution

    |