Home
Class 12
MATHS
Let f(x)=a-(x-3)^(8//9) then greatest va...

Let `f(x)=a-(x-3)^(8//9)` then greatest value of f(x) is

A

3

B

a

C

no maximum vlaue

D

non of these

Text Solution

Verified by Experts

The correct Answer is:
B

We have
`f(x)=a-(x-3)^(8//9)`
Clearly `(x-3)^(8//9) gt 0 " for all " x in R`
`rArr f (x) le a " for all " x in R `
Hence the reastest value of f(x) is a
Promotional Banner

Topper's Solved these Questions

  • MAXIMA AND MINIMA

    OBJECTIVE RD SHARMA|Exercise Section II - Assertion Reason Type|7 Videos
  • MAXIMA AND MINIMA

    OBJECTIVE RD SHARMA|Exercise Exercise|50 Videos
  • MAXIMA AND MINIMA

    OBJECTIVE RD SHARMA|Exercise Chapter Test|30 Videos
  • MATHEMATICAL REASONING

    OBJECTIVE RD SHARMA|Exercise Chapter Test|20 Videos
  • MEASURES OF CENTRAL TENDENCY

    OBJECTIVE RD SHARMA|Exercise Chapter Test|21 Videos

Similar Questions

Explore conceptually related problems

If f(x)=a-(x-3)^(8//9) , then the maximum value of f(x) is

Let f(x)=(kx)/(x+1) then the value of k such that f(x) is

Let f(x) = cos^(2) x + cos x +3 then greatest value of f(x) + least value of f(x) is equal to

Let f(x^(3))=x^(4)+x^(5)+x+1, then the value of f(8)

Let f(x)=x^(2)-ax+3a-4 and g(a) be the least value of f(x) then the greatest value of g(a)

Let f(x)=(9^(x))/(9^(x)+3) then find the value of f((1)/(2006))+f((2)/(2006))+f((3)/(2006))+...+f((2005)/(2006))

Let f(x)=x^(3)e^(-3x),x>0. Then the maximum value of f(x) is

Let f(x)=2x^(3)-9x^(2)+12x+8, the number of values of x for which y=f(f(x)) attains local extremum is/are

Let f (x- = tan ^(-1) ((1-x)/(1+x)). Then difference of the greatest and least value of f (x) on [0,1] is:

Let f (x)= tan/x, then the value of lim_(x->oo) ([f(x)]+x^2)^(1/({f(x)})) is equal to (where [.] , {.} denotes greatest integer function and fractional part functions respectively) -

OBJECTIVE RD SHARMA-MAXIMA AND MINIMA -Section I - Solved Mcqs
  1. P=x^3-1/x^3, Q=x-1/x x in (1,oo) then minimum value of P/(sqrt(3)Q^2...

    Text Solution

    |

  2. Let f(x) = cos 2pix + x -[x]([*] denotes the greatest integer function...

    Text Solution

    |

  3. Let f(x)=a-(x-3)^(8//9) then greatest value of f(x) is

    Text Solution

    |

  4. A function f such that f'(a)=f''(a)=….=f^(2n)(a)=0 , and f has a l...

    Text Solution

    |

  5. Let f(x)={{:(3x^2-2x+10, x lt 1),(-2,x gt 1):} The set of values of ...

    Text Solution

    |

  6. The maximum value of cos (int(2x)^(x^(2)) e^t sin^2 " t dt ")

    Text Solution

    |

  7. Let f(x)= {{:(1+ sin x, x lt 0 ),(x^2-x+1, x ge 0 ):}

    Text Solution

    |

  8. Let f(x)=x^(n+1)+ax^n, "where " a gt 0. Then, x=0 is point of

    Text Solution

    |

  9. The greph of y=x^3+ax^2+bx+c has no extemun if and only if

    Text Solution

    |

  10. If f(x) =int(x)^(x^2) (t-1)dt, 1 le x le 2 then the greatest value of ...

    Text Solution

    |

  11. If the parabola y=ax^2+bx+c has vertex at(4,2)and a in [1,3] then the...

    Text Solution

    |

  12. Let f(X)=In (2x -x^2)+ sin (pix)/(2). Then which one of the following ...

    Text Solution

    |

  13. If alpha and beta respectively the minmum and minimum values of the fu...

    Text Solution

    |

  14. Let f(x)={{:(x^2+4x "," -3 le x le 0),(-sin x ","0 lt x le pi//2 ),(...

    Text Solution

    |

  15. If alpha be the number of solutions of the equation [sin x] =|x| ) and...

    Text Solution

    |

  16. Let f(x1,x2,x3,x4)=x1^2+x2^2+x3^2+x4^2-2(x1+x2+x3+x4)+10 and x1,x3 i...

    Text Solution

    |

  17. Let f,g and h be real-valued functions defined on the interval [0,1] b...

    Text Solution

    |

  18. Let f be a function defined on R (the set of all real numbers) such th...

    Text Solution

    |

  19. Let f:R to R be defined by f(x)={{:(2k-2x",",ifxle-1),(2x+3",",iffxg...

    Text Solution

    |

  20. For e in (0,(5pi)/(2)) " define " f(x)= int(0)^(x) sqrt(t) sin t dt ...

    Text Solution

    |