Home
Class 12
MATHS
Let f(x)=x^(n+1)+ax^n, "where " a gt 0. ...

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

A

local minimum for any integer n

B

local minimum if n is an even integer

C

local maximum if n is an even integer

D

local minimum if n is am odd interger

Text Solution

Verified by Experts

The correct Answer is:
C
We have
`f(x)=x^(n+1)+ax^n`
`rArr f(x) =(n+1)x^n +nax^(n-1)`
`rArr f(x)=[(n+1)x+a]x^(n-1)`
If n is even , then
`(LHD at x =0 ) gt 0 and (RHD at x=0)lt 0 `
Thus f(x) has a local maximum at x=0
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

Let f(x)=(2x+1)/(x),x!=0, where

The range of f(x) =a^(x) ," where " a gt 0 is

If f(x)=(a-x^(n))^(1//n),"where a "gt 0" and "n in N , then fof (x) is equal to

Let f(x)=ax^(2)-b|x| , where a and b are constant . Then at x=0 , f(x) has

Let f(x) =ax^(2) -b|x| , where a and b are constants. Then at x = 0, f (x) is

Let f(x)=x^(2) and g(x)=sin x for all x in R. Then the set of all x satisfying ( fogogo f)(x)=(gogof)(x), where (fog)(x)=f(g(x)) is +-sqrt(n pi),n in{0,1,2,...}+-sqrt(n pi),n in{1,2,...}(pi)/(2)+2n pi,n in{...,-2,-1,0,1,2...}2n pi,n in{...,-2,-1,0,1,2,...}

If f(x)=(a-n^(n))^(1//n) where a gt 0 and n in N , then f[f(x)] is equal to :

OBJECTIVE RD SHARMA-MAXIMA AND MINIMA -Section I - Solved Mcqs
  1. The maximum value of cos (int(2x)^(x^(2)) e^t sin^2 " t dt ")

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  11. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. Let p(x) be a real polynomial of least degree which has a local maximu...

    Text Solution

    |

  17. Let I RvecI R be defined as f(x)=|x|++x^2-1|dot The total number of po...

    Text Solution

    |

  18. If f(x) = int(0)^(x) e^(t^2)(t-2)(t-3) dt " for all " x in (0,oo) t...

    Text Solution

    |

  19. The function f(x)=2|x|+|x+2|=||x|2|-2|x|| has a local minimum or a loc...

    Text Solution

    |

  20. Let f:[0,1] rarr R be a function . Suppose the fuction f is twice diff...

    Text Solution

    |