Home
Class 12
MATHS
If f(x)=alog|x|+b x^2+x has extreme valu...

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 .

A

a=2,b=-1

B

a=2,b=`-1//2`

C

a=-2,b=`1//2`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
2
We have `f(X) =a log|x|+bx^(2) +x`
or `f(X) =(a)/(x)+2bx+1`
since f(X) attains its extremum values at x=1,2
f(-1) =0 and f(X) =0
or -a-2b+1 and `(a)/(2)`+4b+1=0 or a =2 and b =-`1//2`
Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|48 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE ENGLISH|Exercise Numerical Value Type|24 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE ENGLISH|Exercise Concept Application Exercise 6.7|5 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Single Correct Answer Type|46 Videos

  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE ENGLISH|Exercise Comprehension Type|6 Videos

Similar Questions

Explore conceptually related problems

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

The function y=alogx+b x^2+x has extreme values at x=1 and x=2 . 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.

The function y=alogx+bx^2+x has extreme values at x=1,2.Find a and b

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

If f(x) = x^(3) + a x^(2) + b x + c has a maximum at x = -1 and minimum at x = 3. Find a + b.

If h(x)=f(x)+f(-x), " then " h(x) has got and extreme value at a point where f'(x) is

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).

The function f(x)=sqrt(a x^3+b x^2+c x+d) has its non-zero local minimum and local maximum values at x=-2 and x = 2 , respectively. If a is a root of x^2-x-6=0 , then find a,b,c and d.

Let f(x)=(x^2-1)^n(x^2+x+1) then f(x) has local extremum at x=1 when (a) n=2 (b) n=3 (c) n=4 (d) n=6

CENGAGE ENGLISH-MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS-Exercise
  1. f: RvecR ,f(x) is differentiable such that f(f(x))=k(x^5+x),k!=0)dot T...

    Text Solution

    |

  2. The value of a for which the function f(x)=asinx+(1/3)sin3x has an ext...

    Text Solution

    |

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

    Text Solution

    |

  4. If a function f(x) has f^(prime)(a)=0a n df^(a)=0, then (a) x=a is a...

    Text Solution

    |

  5. The function f(x)=sin^4x+cos^4x increasing if 0<x<pi/8 (b) pi/4<x<(3p...

    Text Solution

    |

  6. The function f(x)=sin^4x+cos^4x increasing if 0<x<pi/8 (b) pi/4<x<(3p...

    Text Solution

    |

  7. If f(x)=x^5-5x^4+5x^3-10 has local maximum and minimum at x=p and x=q ...

    Text Solution

    |

  8. Let P(x)=a0+a1x^2+a2x^4++an x^(2n) be a polynomial in a real variable ...

    Text Solution

    |

  9. Let f(x)={(|x|,for 0<|x|lt=2), (1,"for"x=0):} Then at x=0, f(x) has ...

    Text Solution

    |

  10. If f(x)=x^3+b x^2+c x+d and 0<b^2<c , then f(x) is a strictly increasi...

    Text Solution

    |

  11. If f(x)={(sin(x^(2)-3x),xle0 6x+5x^(2),xgt0 then at x=0, f(x) is?

    Text Solution

    |

  12. The greatest value of f(x)=cos(x e^([x])+7x^2-3x),x in [-1,oo], is (wh...

    Text Solution

    |

  13. The function f(x)=(4sin^2x-1)^n(x^2-x+1),n in N , has a local minimum...

    Text Solution

    |

  14. The true set of real values of x for which the function f(x)=xlnx-x+1 ...

    Text Solution

    |

  15. All possible value of f(x)=(x+1)^(1/3)-(x-1)^(1/3) on [0,1] is 1 (b) ...

    Text Solution

    |

  16. The function f(x)=(ln(pi+x))/(ln(e+x)) is

    Text Solution

    |

  17. If the function f(x)=2x^3-9ax^2+12a^2x+1, where a gt 0, attains its m...

    Text Solution

    |

  18. Let f(x)={x+2,-1lelt0 1,x=0 (x)/(2),0ltxle1

    Text Solution

    |

  19. If f(x)={sin^(-1)(sinx),xgt0 (pi)/(2),x=0,then cos^(-1)(cosx),xlt0

    Text Solution

    |

  20. A function f is defined by f(x)=|x|^m|x-1|^nAAx in Rdot The local max...

    Text Solution

    |