Home
Class 12
MATHS
f(x)={(a x(x-1)+b ,, x<1),(x-1 ,, 1lt=xl...

`f(x)={(a x(x-1)+b ,, x<1),(x-1 ,, 1lt=xlt=3),(p x^2+q x+2 ,, x >3):}` Find the values of the constants `a,b, p \ a n d \ q` so that all the following conditions are satisfied `f(x)` is continuous for all `x`, `f^(prime)(1)` does not exist and `f^(prime)(x)` is continuous at `x=3`

Promotional Banner

Topper's Solved these Questions

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|102 Videos

  • COORDINATE SYSTEM

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|2 Videos

Similar Questions

Explore conceptually related problems

A function f(x) satisfies the following property: f(xdoty)=f(x)f(y)dot Show that the function f(x) is continuous for all values of x if it is continuous at x=1.

Let f(x+y)=f(x)+f(y) for all xa n dydot If the function f(x) is continuous at x=0, show that f(x) is continuous for all xdot

The values of constants a and b so as to make the function f(x)={(1/|x|, |x|ge1),(ax^2+b, |x|lt1):} , continuous as well as differentiable for all x, are

A function f(x) satisfies the following property: f(x+y)=f(x)f(y)dot Show that the function is continuous for all values of x if its is continuous at x=1.

Suppose that f(x) is a differentiable function such that f'(x) is continuous, f'(0) = 1 and f"(0) does not exist. Let g(x) = xf'(x). Then

Find the value of f(0) so that the function. f(x)=(sqrt(1+x)-1+x3)/x becomes continuous at x=0

A single valued function f(x) of x defined in [a, b] satisfies the following conditions : (i) f(x) is continuous in [a, b] (ii) f'(x) exists in (a, b) (iii) f(a)=f(b) Then, Rolle's theorem is applicable to f(x), if -

Suppose that f(x) is a differentiable function such that f'(x) is continuous, f'(0)=1 and f''(0) does not exist. Let g(x) = xf'(x). Then

Suppose that f(x) is a differentiable function such that f'(x) is continuous, f'(0)=1 and f''(0) does not exist. Let g(x)=xf'(x) . Then-

Find the relationship between a and b so that the function f defined by f(x)={{:(ax+1," if "x le 3),(bx+3," if "x gt 3):} is continuous at x=3.

CENGAGE PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. Let f be a continuous function defined onto [0,1] with range [0,1]. S...

    Text Solution

    |

  2. Let f be continuous on the interval [0,1] to R such that f(0)=f(1)dot ...

    Text Solution

    |

  3. f(x)={(a x(x-1)+b ,, x<1),(x-1 ,, 1lt=xlt=3),(p x^2+q x+2 ,, x >3):} ...

    Text Solution

    |

  4. Find the values of a and b if f(x)={a+sin^(-1)(x+b), xgeq1 and x ,x<1 ...

    Text Solution

    |

  5. Discuss the differentiability of y=sin^(-1)|sinx|

    Text Solution

    |

  6. Discuss the differentiability of f(x)=m a x{2sinx ,1-cosx}AAx in (0,...

    Text Solution

    |

  7. Discuss the differentiability of f(x)="max"{x^2-3x+2,2-|x-1|}

    Text Solution

    |

  8. Discuss the differentiability of f(x)=e^(-|x|)

    Text Solution

    |

  9. If f(x)={x ,xlt=1,x^2+b x+c ,x >1 find b and c if function is continu...

    Text Solution

    |

  10. Test the continuity and differentiability of the function f(x)=|(x+1/2...

    Text Solution

    |

  11. Let f(x)={(log(1+x)^(1+x)-x)/(x^2)}dot Then find the value of f(0) so ...

    Text Solution

    |

  12. Find the points of discontinuity of the function: f(x)=[[x]]-[x-1],w h...

    Text Solution

    |

  13. let f(x)=(lncosx)/{(1+x^2)^(1/4)-1} if x > 0 and f(x)=(e^(sin4x)-1)/(l...

    Text Solution

    |

  14. What value must be assigned to k so that the function f(x)={(x^4-25...

    Text Solution

    |

  15. Let f(x) be a function defined as f(x)={(x^2-1)/(x^2-2|x-1|-1),x!=1 ...

    Text Solution

    |

  16. If the function f(x)={(Ax-B ,, x le 1),(3x ,,1 lt x lt 2),(Bx^2-A ,, ...

    Text Solution

    |

  17. Let : f(x)={((a+3cosx)/(x^2) ,, x<0),(btan(pi/([x+3])) ,, xgeq0):} If...

    Text Solution

    |

  18. Let : f(x)={(sina x^2)/(x^2),x!=0 3/4+1/(4a),x=0 for what values of...

    Text Solution

    |

  19. f(x)={|x+1|;xlt=0x ;x >0 and g(x)={|x|+1;xlt=1-|x-2|;x >1 Draw its g...

    Text Solution

    |

  20. f(x)={cos^(-1){cotx), x<pi/2 pi[x]-1, x >pi/2 where [dot] represe...

    Text Solution

    |