Home
Class 12
MATHS
The absolute maximum and minimum values ...

The absolute maximum and minimum values of functions can be found by their monotonic and asymptotic behaviour provided they exist. We may agree that finite limits values may be reagarded as absolute maximum or minimum. For instance the absolute maximum value of `(1)/(1+x^(2))` is unity. It is attained at x=0 while absolute maximum value of the same functions is zero which is a limiting value of `(xrarrooorxrarr-oo)`
The function `x^(4)-4x+1` will have.

A

have absolute maximum value `-(1)/(2)`

B

has absolute minimum value `-(25)/(2)`

C

not lie between `-(25)/(2)and-(1)/(2)`

D

always be negative

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

The absolute maximum and minimum values of functions can be found by their monotonic and asymptotic behaviour provided they exist. We may agree that finite limits values may be reagarded as absolute maximum or minimum. For instance the absolute maximum value of (1)/(1+x^(2)) is unity. It is attained at x=0 while absolute maximum value of the same functions is zero which is a limiting value of (xrarrooorxrarr-oo) The absolute minimum and maximum values of the function (x^(2)-x+1)/(x^(2)+x+1) is

The absolute maximum and minimum values of functions can be found by their monotonic and asymptotic behaviour provided they exist. We may agree that finite limits values may be reagarded as absolute maximum or minimum. For instance the absolute maximum value of (1)/(1+x^(2)) is unity. It is attained at x=0 while absolute maximum value of the same functions is zero which is a limiting value of (xrarrooorxrarr-oo) The absolute minimum value of the function (x-2)/(sqrt(x^(2)+1)) is

Find the absolute minimum value of |x|

Find the maximum value of the function x * e^(-x) .

Find the maximum value of the function x^(1//x) .

Write the maximum and minimum values of costheta .

Find the absolute value of -(12)/(29)

If x+y=1 then find the maximum value of the function xy^2

Find the absolute value of (23)/(17)

Write the maximum and minimum values of sintheta .

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

    |