Home
Class 12
MATHS
Let a , b in R be such that the function...

Let a , b in R be such that the function f given by`f(X) = ln |x|+bx^(2)+asx,xne0` has extreme values at x=-1 and at x=2
Statement 1: f has local maximum at x =-1 and at x =2
statement 2: a =`1/2` and b = `(-1)/(2)`.

A

Statement I is false, Statement II is true

B

Statement I is true, Statement II is true, Statement II is a correct explanation of Statement I

C

Statement I is true, Statement II is true, Statement II is not a correct explanation of Statement I

D

Statement I is true, Statement II is false.

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS ENGLISH|Exercise MAXIMA AND MINIMA EXERCISE 6|2 Videos

  • MATRICES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|49 Videos

  • PAIR OF STRAIGHT LINES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

Similar Questions

Explore conceptually related problems

Let a, b R be such that the function f given by f(x)""=""ln""|x|""+""b x^2+""a x ,""x!=0 has extreme values at x""=""1 and x""=""2 . Statement 1: f has local maximum at x""=""1 and at x""=""2 . Statement 2: a""=1/2"and"b=(-1)/4 (1) Statement 1 is false, statement 2 is true (2) Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1 (3) Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1 (4) Statement 1 is true, statement 2 is false

If f(x)=alog|x|+b x^2+x has extreme values at x=-1 and at x=2 , then find a and b .

If f(x)=alog|x|+b x^2+x has extreme values at x=-1 a n d a t x=2, then find a and b .

If f(x) =X^(3) + ax^(2) +bx +c has extreme values at x=-1 and x=3 . Find a,b,c.

let f(x)=(x^2-1)^n (x^2+x-1) then f(x) has local minimum at x=1 when

The function f(x)=[log (x-1)]^(2) (x-1)^(2) has :

Let f: R->R be a function given by f(x)=x^2+1. Find: f^(-1){-5}

Let f: R->R be a function given by f(x)=x^2+1. Find: f^(-1){26}

Let f(x) be the function given by f(x)=arc cos ((1-x^(2))/(1+x^(2))).Then

If the function f(x) = axe^(bx^(2)) has maximum value at x=2 such that f(2) =1 , then find the values of a and b

ARIHANT MATHS ENGLISH-MONOTONICITY MAXIMA AND MINIMA-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If the function g:(-oo,oo)->(-pi/2,pi/2) is given by g(u)=2tan^-1(e^u)...

    Text Solution

    |

  2. The second degree polynomial f(x), satisfying f(0)=o, f(1)=1,f'(x)gt...

    Text Solution

    |

  3. If f(x)=x^3+bx^2+cx+d and 0<b^2<c, then

    Text Solution

    |

  4. If f(x)=x^2+2b x+2c^2 and g(x)= -x^2-2c x+b^2 are such that min f(x...

    Text Solution

    |

  5. The length of the longest interval in which the function 3sinx-4sin^3x...

    Text Solution

    |

  6. If f(x)=e^(1-x) then f(x) is

    Text Solution

    |

  7. The maximum value of (cosalpha(1))(cos alpha(2))...(cosalpha(n)), un...

    Text Solution

    |

  8. If f(x) = {{:(e ^(x),,"," 0 le x lt 1 ,, ""), (2- e^(x - 1),,"," 1 lt ...

    Text Solution

    |

  9. If f(x) is a cubic polynomil which as local maximum at x=-1 . If f(2)=...

    Text Solution

    |

  10. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

    Text Solution

    |

  11. about to only mathematics

    Text Solution

    |

  12. Find a point on the curve x^2 + 2y^2 = 6, whose distance from the li...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. The maximum value of the expression (1)/(sin ^(2) theta + 3 sin thet...

    Text Solution

    |

  17. The maximum value of the function f(x)=2x^3-15 x^2+36 x-48 on the set ...

    Text Solution

    |

  18. A wire of length 2 units is cut into two parts which are bent respecti...

    Text Solution

    |

  19. If x =-1 and x=2 ar extreme points of f(x) =alpha log|x|+betax^(2)+x ,...

    Text Solution

    |

  20. Let a , b in R be such that the function f given byf(X) = ln |x|+bx^(2...

    Text Solution

    |