Home
Class 12
MATHS
If the local minimum of the function f(x...

If the local minimum of the function `f(x)=x^(3)-3a^(2)x+4(AA a gt 0)` occurs at `x=lambda (AA lambda gt 1)`, then `a` may take the value

A

`(sqrt3)/(2)`

B

`(2)/(sqrt3)`

C

`(4)/(5)`

D

0

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • NTA JEE MOCK TEST 73

    NTA MOCK TESTS|Exercise MATHEMATICS|25 Videos

  • NTA JEE MOCK TEST 75

    NTA MOCK TESTS|Exercise MATHEMATICS|25 Videos

Similar Questions

Explore conceptually related problems

The length of the longest interval in which the function f(x)=x^(3)-3a^(2)x+4 is decreasing is (AA a gt 0)

The minimum value of the function f(x)=(tanx)/(3+2tanx), AA x in [0, (pi)/(2)) is

Minimum value of the function f(x)=(1+sin x)(1+cos x)AA x in R, is

If the function f(x)=x^(3)-3ax has a local minimum at x=lambda(lambda ge 4) and a in [10, 18] , then the sum of all the possible integral values of a is

If maximum & minimum value of function f(x)=x^(3)-6x^(2)+9x+1 AA x in [0, 2] are M & m respectively, then value of M – 2m is :

Local minimum of f(x) =x+ (1)/(x) , where x gt 0 , is

The complete set of values of a for which the function f(x)=tan^(-1)(x^(2)-18x +a)gt 0 AA x in R is

The area bounded by y=sqrt(1-x^(2)) and y=x^(3)-x is divided by y - axis in the ratio lambda:1(AA lambda gt 1) , then lambda is equal to

NTA MOCK TESTS-NTA JEE MOCK TEST 74-MATHEMATICS
  1. If A = int(0)^((pi)/(2))(sin^(3)x)/(1+cos^(2)s)dx and B=int(0)^((pi)/(...

    Text Solution

    |

  2. The area of the quadrillateral formed by the tangents and normals at t...

    Text Solution

    |

  3. If the local minimum of the function f(x)=x^(3)-3a^(2)x+4(AA a gt 0) o...

    Text Solution

    |

  4. The vertex of the right angle of a right angled triangle lies on the s...

    Text Solution

    |

  5. The differential equation of the family of ellipses having centres alo...

    Text Solution

    |

  6. An equilateral triangle is inscribed in the ellipse whose equation is ...

    Text Solution

    |

  7. The value of Sigma(k=1)^(99)(i^(k!)+omega^(k!)) is (where, i=sqrt(-1)...

    Text Solution

    |

  8. If the fucntion f(x)={{:(asqrt(x+7),,,0lexlt2),(bx+5,,,x ge2):} is di...

    Text Solution

    |

  9. Consider a matrix A=[a(ij)[(3xx3) where, a(ij)={{:(i+2j,ij="even"),(2i...

    Text Solution

    |

  10. Consider a function f(x)=x^(x), AA x in [1, oo). If g(x) is the invers...

    Text Solution

    |

  11. The standard deviation of a distribution is 30. If each observation is...

    Text Solution

    |

  12. The range of the function f(x)=2sqrt(3x^(2)-4x+5) is

    Text Solution

    |

  13. If A, B, C are three events such that P(B)=(4)/(5), P(A nn B nn C^(c )...

    Text Solution

    |

  14. If the line (x-1)/(5)=(y-3)/(2)=(z-3)/(2) intersects the curve x^(2)-y...

    Text Solution

    |

  15. Let A=[(1,0,3),(0,b,5),(-(1)/(3),0,c)], where a, b, c are positive int...

    Text Solution

    |

  16. The value of lim(xrarr(pi)/(6))(2cos(x+(pi)/(3)))/((1-sqrt3tanx)) is e...

    Text Solution

    |

  17. Coefficient of t^(24) in (1+t^(2))^(12)(1+t^(12))(1+t^(24)) is :

    Text Solution

    |

  18. If 1 in (alpha, beta) where alpha, beta are the roots of the equation ...

    Text Solution

    |

  19. Let the function f(x)=|x+1|. The number of values of x in [-2,2] for w...

    Text Solution

    |

  20. If sinx+cosy=(1)/(3) and cos x+siny=(3)/(4), then the value of tan((x-...

    Text Solution

    |