Home
Class 11
MATHS
Let f(x) = (1+b^(2))x^(2) + 2bx + 1 and ...

Let `f(x) = (1+b^(2))x^(2) + 2bx + 1` and let m (b) be the minimum value of f(x). As b varies, find the range of m(b).

A

[0,1]

B

`(0,1/2)`

C

`(1/2,1)`

D

[0,1]

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • MAXIMA & MINIMA

    AAKASH SERIES|Exercise EXERCISE-III|35 Videos

  • MAXIMA & MINIMA

    AAKASH SERIES|Exercise EXERCISE-I|31 Videos

  • MATRICES

    AAKASH SERIES|Exercise LINEAR EQUATIONS - PRACTICE EXERCISE|15 Videos

  • MAXIMA AND MINIMA

    AAKASH SERIES|Exercise ADDITIONAL PRACTICE EXERCISE (LEVEL - II (PRACTICE SHEET )(ADVANCED)) (INTEGER TYPE QUESTIONS)|3 Videos

Similar Questions

Explore conceptually related problems

Let f(x)=cospix+10x+3x^(2)+x^(3),-2lexle3 . The absolute minimum value of f(x) is

Let f(x)=(x-2)(x^(4)-4x^(3)+6x^(2)-4x+1) then value of local minimum of f is

Let f(x)=(arc tanx)^(3)+(arc cotx)^(3) . If the range of f(x) is [a,b) then the value of b/(7a) is

If A=x^(2)+(1)/(x^(2)),B=x-(1)/(x) then minimum value of (A)/(B) is (where x in(-1,0)uu(1,oo))

Theorem : Let f(x)=ax^(2)+bx+c be a quadratic function. If a gt 0 then f(x) has minimum value at x =(-b)/(2a) and the minimum value = (4ac -b^(2))/(4a)

A function f is defined by f(x)= {{:((sin (a + 1) x + sinx)/(x)" if " x lt 0),(c " if " x = 0),(((x + bx^(2))^(1/2)- x^(1/2))/(bx^(3/2)) " if " x gt 0 ):} It f(x) is continuous at x = 0 , find the values of a,b and c .

Theorem: Let f(x)=ax^(2)+bx+c be a quadratic function. If a gt0 then f(x) has minimum value at x=(-b)/(2a) and the minimum value =(4ac-b^(2))/(4a) .

Show that f(x) = ax^(2) + bx + c (a ne0) is maximum at x = -(b)/(2a) when a lt 0 and minimum at x = -(b)/(2a) when a gt 0 . Also find the maximum and minimum values of f(x).

AAKASH SERIES-MAXIMA & MINIMA-EXERCISE-II
  1. The least value of (sin^(-1)x)^3+(cos^(-1)x)^3 is

    Text Solution

    |

  2. If A gt 0, b gt 0 and A+B =pi//3, then the maximum value of tan A tan ...

    Text Solution

    |

  3. Let f(x) = (1+b^(2))x^(2) + 2bx + 1 and let m (b) be the minimum value...

    Text Solution

    |

  4. If f(x) = a log |x| + bx^(2) + x has extreme values at x = -1 and x = ...

    Text Solution

    |

  5. The condition that f(x) =ax^3+bx^2+cx+d has no extreme value is

    Text Solution

    |

  6. The minimum value of x^(logx) is

    Text Solution

    |

  7. Maximum value of f(x)=(2+x)^(1//3)(1-x)^(2//3) is

    Text Solution

    |

  8. If f^1(x)=(x-a)^8(x-b)^(11) then

    Text Solution

    |

  9. Let f(x) =a0+a1x^2+a2x^4+…….+anx^(2n) be a polynomial in x in R with 0...

    Text Solution

    |

  10. The function f(x)=4x^5-25x^4+40x^3-10 has

    Text Solution

    |

  11. The function x (x-1) (x-2) attains its maximum value when x is

    Text Solution

    |

  12. If x+y = 6543298 and x^(11)y^5 is maximum then the ratio of the number...

    Text Solution

    |

  13. If xgt0,ygt0,x+y=3 and xy is maximum then the maximum value of xy is

    Text Solution

    |

  14. A line segment of length 8cm is divided into two parts AP and PB by a ...

    Text Solution

    |

  15. The value of 'a' for which the function f(x) =a sin x+1/3 sin 3x has a...

    Text Solution

    |

  16. The real number x when added to its inverse gives the minimum value of...

    Text Solution

    |

  17. The difference of two positive numbers is 10 . If the square of the gr...

    Text Solution

    |

  18. The positive real number which most exceeds its cube is

    Text Solution

    |

  19. The points on y=x^2+7x+2 which is closest to the line y=3x-3 is

    Text Solution

    |

  20. If x is real, then the minimum value of y=(x^(2)-x+1)/(x^(2)+x+1) is

    Text Solution

    |