Home
Class 12
MATHS
The minimum value that f(x)=4x^2-4x+1...

The minimum value that
`f(x)=4x^2-4x+11+sin 3 pi x` attains is

A

12

B

10

C

8

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
We have
`f(x)=4x^2-4x+11+ sin 3 pi x `
`rArr f(x)=4(x-1/2)^2+10+sin3 pi x`
we obsen that `4 (x-1/2)^2 ` takes its least value -1
Hence `f(x )` attains its least value 9 at `x= 1/2`
Promotional Banner

Topper's Solved these Questions

  • MAXIMA AND MINIMA

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Solved Mcqs|72 Videos

  • MAXIMA AND MINIMA

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|7 Videos

  • MATHEMATICAL REASONING

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|20 Videos

  • MEASURES OF CENTRAL TENDENCY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|21 Videos

Similar Questions

Explore conceptually related problems

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

The minimum value of f(x)=e^((x^4-x^3+x^2)) is

The minimum value of the function f(x)=(3 sin x - 4 cos x - 10)(3 sin x + 4 cos x-10) , is

Find the maximum and minimum values of the function f(x) = x+ sin 2x, (0 lt x lt pi) .

Find the maximum and the minimum values of f(x)=sin3x+4,\ \ x in (-pi//2,\ pi//2) , if any.

The minimum value of f(x)= "sin"x, [(-pi)/(2),(pi)/(2)] is

The minimum value of f(x)-sin^(4)x+cos^(4)x,0lexle(pi)/(2) is

Find the maximum and minimum values of f(x)=x+sin2x in the interval [0,\ 2pi]

Minimum value of 4x^2-4x|sin theta|-cos^2 theta is equal

Find the maximum and minimum values of f(x)=|sin4x+3| on R , if any, without using derivatives.

OBJECTIVE RD SHARMA ENGLISH-MAXIMA AND MINIMA -Chapter Test
  1. The minimum value that f(x)=4x^2-4x+11+sin 3 pi x attains is

    Text Solution

    |

  2. The maximum value of ((1)/(x))^(2x^(2)) is

    Text Solution

    |

  3. If a x^2+b/xgeqc for all positive x where a >0 and b >0, show that 27 ...

    Text Solution

    |

  4. The greatest value of the funxtion f(x)=xe^(-x) " in " [0,oo] is

    Text Solution

    |

  5. Let f(x)=x^3-6x^2+12x-3 . Then at x=2 f(x) has

    Text Solution

    |

  6. In the right triangle BAC, angle A=pi/2 and a+b=8. The area of the tr...

    Text Solution

    |

  7. The range of values of a for which the function f(x)=(a^2-7a+12)cosx...

    Text Solution

    |

  8. If the function f(x) = (2a-3)(x+2 sin3)+(a-1)(sin^4x+cos^4x)+log 2...

    Text Solution

    |

  9. The function y=(ax+b)/(x-1)(x-4) has turning point at P(2,-1) Then fin...

    Text Solution

    |

  10. Find the least value of the expressions 2log(10)x-log(x)0.01, where xg...

    Text Solution

    |

  11. The maximum value of the function f(x) given by f(x)=x(x-1)^2,0ltxlt...

    Text Solution

    |

  12. The least value of a for which the equation 4/(sinx)+1/(1-sinx)=a has ...

    Text Solution

    |

  13. The minimum value of f(x)=e^((x^4-x^3+x^2)) is

    Text Solution

    |

  14. Let f(x)=a/x+x^2dot If it has a maximum at x=-3, then find the value o...

    Text Solution

    |

  15. Find the maximum value of 4sin^(2)x+3cos^(2)x+sin""(x)/(2)+cos""(x)/(2...

    Text Solution

    |

  16. The least value of the f(x) given by f(x)=tan^(-1)x-1/2 logex " in t...

    Text Solution

    |

  17. The slope of the tangent to the curve y=e^x cosx is minimum at x= a,0 ...

    Text Solution

    |

  18. The value of a for which the function f(x)={{:(tan^(-1)a -3x^2" , " ...

    Text Solution

    |

  19. The minimum value of 27^(cos3x)81^(sin3x) is

    Text Solution

    |

  20. If f(x)=(x^2-1)/(x^2+1) . For every real number x , then the minimum v...

    Text Solution

    |

  21. f(x) = |x|+|x-1| +|x-2|, then which one of the following is not correc...

    Text Solution

    |