Home
Class 12
MATHS
If f(x)={{:(,ax^(2)-b,|x|lt 1),(,(1)/(|x...

If `f(x)={{:(,ax^(2)-b,|x|lt 1),(,(1)/(|x|),|x| ge1):}` is differentiable at x=1, then

A

`a=(1)/(2),b=-(1)/(2)`

B

`a=-(1)/(2),b=-(3)/(2)`

C

`a=b=(1)/(2)`

D

`a=b=-(1)/(2)`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|13 Videos

  • COMPLEX NUMBERS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|58 Videos

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test 2|56 Videos

Similar Questions

Explore conceptually related problems

If f(x)={{:(a+tan^(-1)(x-b),,,x ge1),((x)/(2),,,xlt1):} is differentiable at x = 1, then 4a-b can be

If the function f(x)={{:(,-x,x lt 1),(,a+cos^(-1)(x+b),1 le xle 2):} is differentiable at x=1, then (a)/(b) is equal to

Let a and b be real numbers such that the function g(x)={{:(,-3ax^(2)-2,x lt 1),(,bx+a^(2),x ge1):} is differentiable for all x in R Then the possible value(s) of a is (are)

If f(x)={{:(,e^(x),x lt 2),(,ax+b,x ge 2):} is differentiable for all x in R , them

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

Let f(x)={{:(x^(2)-ax+1",", x lt 0),(b(1-x)^(3)",", x ge0):} . If is a differentiable function, then the ordered pair (a, b) is

If f(x)={{:(,ax^(2)-b,ale xlt 1),(,2,x=1),(,x+1,1 le xle2):} then the value of the pair (a,b) for which f(x) cannot be continuous at x=1, is

Show that the function f(x)={:{(x^2+2", " xge1),(2x+1", " x lt 1 ):} is always differentiable at x=1

Let f(x)={{:(,x^(3),x lt 1),(,ax^(2)+bx+c,:x ge 1):} . If f''(1) exists, then the value of (a^(2)+b^(2)+c^(2)) is

Let f(x)={{:( 0,x=0),(x^(2) sin pi//2x,|x| lt 1),(x|x|, |x| ge 1):} . Then , f(x) is

OBJECTIVE RD SHARMA ENGLISH-CONTINUITY AND DIFFERENTIABILITY-Exercise
  1. Let f(x) be defined on R such that f(1)=2,f(2)=8 and f(u+v)=f(u)+kuv-2...

    Text Solution

    |

  2. Let f(x) be a function satisfying f(x+y)=f(x) + f(y) and f(x) = x...

    Text Solution

    |

  3. If f(x)={{:(,ax^(2)-b,|x|lt 1),(,(1)/(|x|),|x| ge1):} is differentiabl...

    Text Solution

    |

  4. If f(x)=(x-x(0)) phi (x) and phi(x) is continuous at x=x(0). Then f'(...

    Text Solution

    |

  5. Let f (x+y) =f (x) f (y) for all x and y, and f(5)=2, f'(0)=3, then f ...

    Text Solution

    |

  6. If f be a function satisfying f(x+y)=f(x)+f(y),AAx,yinR. If f(1) = k, ...

    Text Solution

    |

  7. Let f (x + y) = f(x) f(y) for all x, y, in R, suppose that f(3) = 3...

    Text Solution

    |

  8. Let f(x+y)=f(x)+f(y) and f(x)=x^2g(x)AA x,y in R where g(x) is continu...

    Text Solution

    |

  9. Let f(x+y)=f(x)f(y) for all x, y epsilon R and f(x)=1+x phi (x) l n 2 ...

    Text Solution

    |

  10. Let f(x+y)=f(x) f(y) and f(x)=1+(sin 2x)g(x) where g(x) is continuous....

    Text Solution

    |

  11. Let f(x+y)=f(x) f(y) and f(x)=1+(sin 2x)g(x) where g(x) is continuous....

    Text Solution

    |

  12. Let g(x) be the inverse of an invertible function f(x) which is differ...

    Text Solution

    |

  13. Let g(x) be the inverse of f(x) and f'(x)=1/(1+x^(3)).Find g'(x) in te...

    Text Solution

    |

  14. Let f(x)={{:(,x^(n)sin\ (1)/(x),x ne 0),(,0,x=0):} Then f(x) is contin...

    Text Solution

    |

  15. If for a continuous function f,f(0)=f(1)=0,f'(1)=2 and y(x)=f(e^(x))e^...

    Text Solution

    |

  16. Let f(x) be a function such that f(x+y)=f(x)+f(y) and f(x)=sin x g(x)...

    Text Solution

    |

  17. Let f(0,pi) to R be defined as f(x)={{:(,(1-sinx)/((pi-2x)^(2)).(In si...

    Text Solution

    |

  18. If f(x)=(e^(2x) - (1+4x)^(1//2))/(ln(1-x^2)) for x != 0, then f has

    Text Solution

    |

  19. Let f(x)={{:(,(ex^(2)-(2)/(pi)sin^(-1)sqrt(1-x))/(In(1+sqrtx)),x in (0...

    Text Solution

    |

  20. Let f(x)={{:(,x^(3),x lt 1),(,ax^(2)+bx+c,:x ge 1):}. If f''(1) exists...

    Text Solution

    |