Home
Class 12
MATHS
The minimum value of f(x)=x^4-x^2-2x+6 i...

The minimum value of `f(x)=x^4-x^2-2x+6` is (a) 6 (b) 4 (c) 8 (d) none of these

Text Solution

AI Generated Solution

To find the minimum value of the function \( f(x) = x^4 - x^2 - 2x + 6 \), we will follow these steps: ### Step 1: Find the first derivative We start by differentiating the function \( f(x) \): \[ f'(x) = \frac{d}{dx}(x^4 - x^2 - 2x + 6) \] ...
Promotional Banner

Topper's Solved these Questions

  • LINEAR PROGRAMMING

    RD SHARMA|Exercise Solved Examples And Exercises|52 Videos

  • MEAN AND VARIANCE OF A RANDOM VARIABLE

    RD SHARMA|Exercise Solved Examples And Exercises|113 Videos

Similar Questions

Explore conceptually related problems

If f(x)= e^(coscos^-1x^2+tancot^-1 x^2), then minimum value of f(x) is (A) e (B) e^2 (C) e^(2/3 (D) none of these

Minimum value of of f (x)=2x^(2)-4x+5is

Minimum value of f(x)=2x^(2)-4x+5 is 1 (b) -1(c)11 (d) 3

Find the minimum value of f(X)=x^(2)-5x+6 .

Local minimum value of f(x)=x^(3)-3x^(2)-24x+5 is a) 33 b) -75 c) -2 d) 4

Let |x2xx^2x6xx6|=a x^4+b x^3+c x^2+dx+edot Then, the value of 5a+4b+3c+2d+e is equal 0 (b) -16 (c) 16 (d) none of these

Period of f(x)=sin^4x+cos^4x is- pi b. pi/2 c. 2pi d. none of these

If x=y=2z and xyz=256, then x=? (a) 2 (b) 4 (c) 8 (d) None of these

Let f(x)=(x-a)^(2)+(x-b)^(2)+(x-c)^(2) Then,f(x) has a minimum at x=(a+b+c)/(3)(b)(1)/(2) (c) (1)/(8) (d) none of these

For certain curves y= f(x) satisfying [d^2y]/[dx^2]= 6x-4, f(x) has local minimum value 5 when x=1. 9. Number of critical point for y=f(x) for x € [0,2] (a) 0 (b)1. c).2 d) 3 10. Global minimum value y = f(x) for x € [0,2] is (a)5 (b)7 (c)8 d) 9 11 Global maximum value of y = f(x) for x € [0,2] is (a) 5 (b) 7 (c) 8 (d) 9

RD SHARMA-MAXIMA AND MINIMA-Solved Examples And Exercises
  1. For the function f(x)=x+1/x x=1 is a point of maximum (b) x=-1 is a p...

    Text Solution

    |

  2. Let f(x)=x^3+3x^2-9x+2 . Then, f(x) has a maximum at x=1 (b) a minimum...

    Text Solution

    |

  3. The minimum value of f(x)=x^4-x^2-2x+6 is (a) 6 (b) 4 (c) 8 (d) none o...

    Text Solution

    |

  4. The number which exceeds its square by the greatest possible quanti...

    Text Solution

    |

  5. Let f(x)=(x-a)^2+(x-b)^2+(x-c)^2 . Then, f(x) has a minimum at x= (a+...

    Text Solution

    |

  6. The sum of two non-zero numbers is 8, the minimum value of the sum ...

    Text Solution

    |

  7. The function f(x)=sum(r=1)^5(x-r)^2 assuming minimum value at x= ...

    Text Solution

    |

  8. At x=(5pi)/6,\ \ f(x)=2sin3x+3cos3x is (a) 0 (b) maximum (c) minimum (...

    Text Solution

    |

  9. If x lies in the interval [0,\ 1] , then the least value of x^2+x+1...

    Text Solution

    |

  10. The least value of the function f(x)=x^3-18 x^2+96 x in the interval [...

    Text Solution

    |

  11. The maximum value of f(x)=x/(4-x+x^2) on [-1,1] is (a)1/4 (b) -1/3...

    Text Solution

    |

  12. Find the point on the curve y^2=4x which is nearest to the point (2, 1...

    Text Solution

    |

  13. If x+y=8 , then the maximum value of x y is (a) 8 (b) 16 (c) 20 (d)...

    Text Solution

    |

  14. The least and greatest values of f(x)=x^3-6x^2+9x in [0,\ 6] , are ...

    Text Solution

    |

  15. f(x)=sin+sqrt(3)cosx is maximum when

    Text Solution

    |

  16. If a cone of maximum volume is inscribed in a given sphere, then th...

    Text Solution

    |

  17. The minimum value of (x^2+(250)/x) is (a) 75 (b) 50 (c) 25 (d) 55

    Text Solution

    |

  18. If f(x)=x+1/x ,\ \ x >0 , then its greatest value is -2 (b) 0 (c) 3...

    Text Solution

    |

  19. If f(x)=1/(4x^2+2x+1) , then its maximum value is (a) 4/3 (b) 2/3 (...

    Text Solution

    |

  20. Let x ,\ y be two variables and x >0,\ \ x y=1 , then minimum value of...

    Text Solution

    |