Home
Class 12
MATHS
find the values of a and b , such that ...

find the values of `a ` and `b` , such that `f(x) ={ax^2+1,xle1 and x^2+ax+b , x gt1` is differentiable at `x=1`

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

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

Find the cofficients a and b such that the following function f is continuous and differentiable at x=+-1: f(x)={{:((1)/(|x|)," when "|x|ge1),(ax^(2)+b," when " |x|lt1):}

Find the least value of a such that the function f given by f(x) = x^(2) + ax + 1 is increasing on [1, 2]?

If f(x)={x ,xlt=1,x^2+b x+c ,x >1 find b and c if function is continuous and differentiable at x=1

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

Determine the values of x for which the following functions fails to be continuous or differentiable f(x) = {((1-x), x lt 1), ((1-x)(2-x), 1lexle2 ), ((3-x), x gt 2):}

If the function f(x)={{:(2x+3",","when "xle1),(ax^(2)+bx",","when "xgt1):} is differentiable everywhere then show that f '(3) =-10

If f(x) = ax^2 + bx + c find a, b so that f(x + 1) = f(x) + x + 1 may hold identically.

If f(x)=e^(ax+b) , find the differentiation of f(x) w.r.tx.

Let a, binR be such that the function f given by f(x)=ln|x|+bx^2+ax,xne0 has extreme values at x = -1 and x = 2 Statement 1:f has local maximum ar x=-1 and x=2. Statement 2: a=1/2 and b=1/4

CENGAGE PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. Discuss the continuity and differentiablity of f(x)=|x+1|+|x|+|x-1|...

    Text Solution

    |

  2. Discuss the differentiability of f(x)="max"{tan^(-1)x ,cot^(-1)x}dot

    Text Solution

    |

  3. find the values of a and b , such that f(x) ={ax^2+1,xle1 and x^2+ax...

    Text Solution

    |

  4. Discuss the differentiability of f(x)=|x[x]| ,-1 < x <= 2

    Text Solution

    |

  5. find the values of a and b , such that f(x) ={ax^2+1,xle1 and x^2+ax...

    Text Solution

    |

  6. Discuss the differentiability of f(x)=cos^(-1)((1-x^2)/(1+x^2))

    Text Solution

    |

  7. Which of the following function is non-differentiable in domain? (a)f(...

    Text Solution

    |

  8. Discuss the continuity of f(x)={1/(e^(x-1)),x!=1; 0,x=1

    Text Solution

    |

  9. Which of the following functions is not continuous AAx in R ?

    Text Solution

    |

  10. Find the value of f(0) so that the function. f(x)=(sqrt(1+x)-1+x^3)/x ...

    Text Solution

    |

  11. If the function f(x)={((x^2-(A+2)x+A)/(x-2), "for" x ne 2),(2, "for"...

    Text Solution

    |

  12. If the function f: R- {0}-> R given by f(x)=1/x-2/(e^(2x)-1) is conti...

    Text Solution

    |

  13. L e t f(x)=(1-tanx)/(4x-pi),x!=pi/4,x in [0,pi/2], Iff(x)i s continuou...

    Text Solution

    |

  14. If f(x)=(tan(pi/4+(log)e x))^((log)x e) is to be made continuous at x=...

    Text Solution

    |

  15. f(x)={(2xtanx-pi/(cosx) ,, x!=pi/2),(k ,, x=pi/2):} i s \ c o n t i n ...

    Text Solution

    |

  16. Discuss the continuity of f(x) ={{:(((x^(2))/|x|,xne0),(0,x=0):}

    Text Solution

    |

  17. Let f(x)={(1+3x)^(1/x), x != 0e^3,x=0 Discuss the continuity of f(x) a...

    Text Solution

    |

  18. Discuss the differentiability of f(x)=||x^2-4|-12|dot

    Text Solution

    |

  19. f(x)=(lim)(n->oo)(sin(pix/2))^(2n) for x >0,x!=1,and f(1)=0. Discuss ...

    Text Solution

    |

  20. Discuss the continuity of f(x)={cot^(-1)x}({dot} represents the fract...

    Text Solution

    |