Home
Class 12
MATHS
Let f(x)=ax^(2)+bx+c,ab,c in R. It is gi...

Let `f(x)=ax^(2)+bx+c,ab,c in R.` It is given `|f(x)|le1,|x|le1`
The possible value of `|a+c|,if(8)/(3)a^(2)+2ab^(2)` is maximum is given by

A

1

B

0

C

2

D

3

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 1|7 Videos
  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 2|4 Videos
  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|29 Videos
  • MATRICES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|49 Videos
  • PAIR OF STRAIGHT LINES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

Similar Questions

Explore conceptually related problems

Let f(x) = ax^2 + bx +C,a,b,c in R .It is given |f(x)|<=1,|x|<=1 The possible value of |a + c| ,if 8/3a^2+2b^2 is maximum, is given by

Let f(x) = ax^2 + bx +C,a,b,c in R .It is given |f(x)|<=1,|x|<=1 The possible value of |a + c| ,if 8/3a^2+2b^2 is maximum, is given by

Let f(x) = ax^(2) - bx + c^(2), b ne 0 and f(x) ne 0 for all x in R . Then

Let f(x) = a x^2 + bx + c , where a, b, c in R, a!=0 . Suppose |f(x)| leq1, x in [0,1] , then

If f(x)=ax^(2)+bx+c and f(-1) ge -4 , f(1) le 0 and f(3) ge 5 , then the least value of a is

If 02 le x le 2 , the maximum value of f(x)=1-x^(2) is

Let |f (x)| le sin ^(2) x, AA x in R, then

Let f (x)= max (x,x ^(2) x ^(3)) in -2 le x le 2. Then:

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) = ax^(2) + bx + c . Consider the following diagram .

ARIHANT MATHS ENGLISH-MONOTONICITY MAXIMA AND MINIMA-EXAMPLE
  1. A solid cylinder of height H has a conical portion of same height and ...

    Text Solution

    |

  2. Statement 1: f(x)=x+cosx is increasing AAx in Rdot Statement 2: If f...

    Text Solution

    |

  3. Consider a DeltaOAB formed by the point O(0,0),A(2,0),B(1,sqrt(3)).P(x...

    Text Solution

    |

  4. Let f(x)=ax^(2)+bx+c,ab,c in R. It is given |f(x)|le1,|x|le1 The po...

    Text Solution

    |

  5. Let f(x)=ax^(2)+bx+c,ab,c in R. It is given |f(x)|le1,|x|le1 The po...

    Text Solution

    |

  6. The absolute maximum and minimum values of functions can be found by t...

    Text Solution

    |

  7. The absolute maximum and minimum values of functions can be found by t...

    Text Solution

    |

  8. Let f(x)={:{(max{t^(3)-t^(2)+t+1,0letlex}",",0lexle1),(min{3-t,1lttlex...

    Text Solution

    |

  9. The graph of derivative of a function f(x) is given (i.e. y=f'(x)). An...

    Text Solution

    |

  10. If a function (continuos and twice differentiable) is always concave u...

    Text Solution

    |

  11. If f(x)={(1)/(x)}andg(x)={x^(2)}, then the number of positive roots sa...

    Text Solution

    |

  12. Match the Statements of Column I with values of Column II.

    Text Solution

    |

  13. Match the Statements of Column I with values of Column II.

    Text Solution

    |

  14. The set of all points where f(x) is increasing is (a,b)cup(c,oo). Find...

    Text Solution

    |

  15. Let f(x) be a cubic polynomial defined by f(x)=x^(3)/(3)+(a-3)x^(2)+...

    Text Solution

    |

  16. If f(x)=max| 2 siny-x|, (where y in R), then find the minimum value o...

    Text Solution

    |

  17. Let f(x)=sin^(-1)((2phi(x))/(1+phi^(2)(x))). Find the interval in whic...

    Text Solution

    |

  18. Find the minimum value of f(x)=|x+2|+|x-2|+|x|.

    Text Solution

    |

  19. The interval to which b may belong so that the functions. f(x)=(1-sq...

    Text Solution

    |

  20. One corner of a long rectangular sheet of paper of width 1 unit is fol...

    Text Solution

    |