Home
Class 12
MATHS
For any real number b, let f (b) denotes...

For any real number b, let f (b) denotes the maximum of `| sin x+(2)/(3+sin x)+b|AAxx x in R.` Then the minimum value of `f (b)AA b in R`is:

A

`1/2`

B

`3/4`

C

`1/4`

D

`1`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (ONE OR MORE THAN ANSWER IS/ARE CORRECT )|29 Videos
  • APPLICATION OF DERIVATIVES

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|15 Videos
  • AREA UNDER CURVES

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise AXERCISE (SUBJECTIVE TYPE PROBLEMS)|8 Videos

Similar Questions

Explore conceptually related problems

Let f(x) = Maximum {sin x, cos x} AA x in R . minimum value of f (x) is

Let f(b) be the minimum value of the expression y=x^(2)-2x+(b^(3)-3b^(2)+4)AA x in R . Then, the maximum value of f(b) as b varies from 0 to 4 is

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

If f:R to R be the function defined by f(x) = sin(3x+2) AA x in R. Then, f is invertible.

Find the maximum and the minimum values of f(x)=3x^2+6x+8,\ \ x in R , if any.

If for the function f(x)=1/4x^2+b x+10 ;f(12-x)=f(x)AAx in R , then the value of ' b ' is-

For a real number x, let [x] denote the greatest integer less than or equal to x. Let f: R -> R be defined as f(x)= 2x + [x]+ sin x cos x then f is

Find the maximum and the minimum values of f(x)=sin(sinx) for all x in R , if any.

Let y=sin^(2)x+cos^(4)x . Then, for all real x (a) the maximum value of y is 2 (b) the minimum value of y is 3/4

If the maximum value of ||x-3| - |x-2|| is a and minimum value of |x-1| + |x-2| is b, then find the value of (a+b).

VIKAS GUPTA (BLACK BOOK) ENGLISH-APPLICATION OF DERIVATIVES -EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. For any real number b, let f (b) denotes the maximum of | sin x+(2)/(3...

    Text Solution

    |

  2. A conical vessel is to be prepared out of a circular sheet of gold of ...

    Text Solution

    |

  3. On [1,e], then least and greatest vlaues of f (x) = x^(2)ln x are m a...

    Text Solution

    |

  4. If f (x)= (px)/(e ^(x)) - (x ^(2))/(2) + x is a decreasing function f...

    Text Solution

    |

  5. L e tf(x)={x e^(a x),xlt=0x+a x^2-x^3,x >0 where a is a positive cons...

    Text Solution

    |

  6. Find sum of all possible values of the real parameter 'b' if the diffe...

    Text Solution

    |

  7. Let 'theta' be the angle in radians between the curves (x ^(2))/(36) +...

    Text Solution

    |

  8. Let set of all possible values of lamda such that f (x)= e ^(2x) - (la...

    Text Solution

    |

  9. Let a,b,c and d be non-negative real number such that a ^(5)+b^(5) le ...

    Text Solution

    |

  10. There is a point (p,q) on the graph of f(x)=x^(2) and a point (r,s) on...

    Text Solution

    |

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

    Text Solution

    |

  12. Let f (x) = int (0)^(x) ((a -1) (t ^(2)+t+1)^(2) -(a+1)(t^(4)+t ^(2) +...

    Text Solution

    |

  13. The numbr of real roots of the equation x ^(2013)+ e ^(2014x) =0 is

    Text Solution

    |

  14. Let the maximum value of expression y= (x ^(4)-x ^(2))/(x ^(6) + 2x ^(...

    Text Solution

    |

  15. The least positive integral value of 'k' for which there exists at lea...

    Text Solution

    |

  16. The coordinates of a particle moving in a plane are given by x (t) = a...

    Text Solution

    |

  17. A tank contains 100 litres of fresh water. A solution containing 1 gm/...

    Text Solution

    |

  18. If f (x) is continous and differentiable in [-3,9] and f'(x) in [-2,8]...

    Text Solution

    |

  19. It is given that f (x) is defined on R satisfying f (1)=1 and for AA ...

    Text Solution

    |

  20. The number of normals to the curve 3y ^(3) =4x which passes through th...

    Text Solution

    |

  21. Find the number of real root (s) of the equation ae ^(x) =1+ x + (x ^(...

    Text Solution

    |