Home
Class 12
MATHS
Let f(x) = x ^3 - 12x. Prove that the eq...

Let `f(x) = x ^3 - 12x`. Prove that the equation `x^3 - 12x - k = 0` has a root `- 2 if k = max f(x)` while it will have a root `2 if k= min f(x)`.

Promotional Banner

Topper's Solved these Questions

  • Maxima and Minima

    A DAS GUPTA|Exercise EXERCISE|59 Videos

  • Main Tests

    A DAS GUPTA|Exercise Exercise|8 Videos

  • Miscellaneous Exercises

    A DAS GUPTA|Exercise Exercise|77 Videos

Similar Questions

Explore conceptually related problems

The value of k so that the equation x^(3)-12x+k=0 has distinct roots in [0,2] is

One of the roots of the equation x^(2)-12x+k=0 is x=3 . The value of k is :

For what values of k does the quadratic equation 4x^(2) - 12x - k =0 have no real roots ?

Let f(x)=x^3-6x^2+12x-3 . Then at x=2 f(x) has

Let f(x)-2x-x^(2),x<=1 then the roots of the equation f(x)=f^(-1)(x) is

" If the equation "2x^(3)-9x^(2)+12x+k=0" has two equal roots then maximum value of "|k|

Let f(x)=x^(3)-x^(2)+12x-3 then at x=2f(x) has

If the roots of the equation 4x^(3)-12x^(2)+11x+k=0 are in A.P.Then K=

If roots of the equation are x^(3)-12x^(2)+kx-48=0 are in AP then find k and equation

A DAS GUPTA-Maxima and Minima-EXERCISE
  1. Show that f(x) = sqrt(e^(x^(2))-1) has its extremum at x = 0. Also me...

    Text Solution

    |

  2. Using examples, prove that the conditiondy/dx = 0 is neither a necessa...

    Text Solution

    |

  3. Let f(x) = x ^3 - 12x. Prove that the equation x^3 - 12x - k = 0 has a...

    Text Solution

    |

  4. If y=a log x +bx^(2)+x has its exteme values at x=-1 and x=2, then fin...

    Text Solution

    |

  5. If y=(a x-b)/((x-1)(x-4)) has a turning point P(2,-1), find the value ...

    Text Solution

    |

  6. Find the shortest distance of the point (0, c) from the parabola y=x^...

    Text Solution

    |

  7. Find the coordinates of a point on the parabola y=x^2+7x+2 which is cl...

    Text Solution

    |

  8. Given an interior point A on the axis of the parabola y ^2 = 2px, (p >...

    Text Solution

    |

  9. Find the coordinates of the point on the curve y=x/(1+x^2) where the t...

    Text Solution

    |

  10. The parametric equations of the curve are x=2t(t^2+3)-3t^2, y=2t(t^2+3...

    Text Solution

    |

  11. A function is defined parametrically as follows :x=t^5-5t^3-20 t+7y=4t...

    Text Solution

    |

  12. Let (h , k) be a fixed point, where h >0,k > 0. A straight line passin...

    Text Solution

    |

  13. A 12-cm-long wire is bent to form a triangle with one of the angles as...

    Text Solution

    |

  14. The largest area of a rectangle which has one side on the x-axis and t...

    Text Solution

    |

  15. Three sides of a trapezium are each equal to k cm. Find the greatest p...

    Text Solution

    |

  16. A statue 4 meters high sits on a column 5.6 meters high . How far f...

    Text Solution

    |

  17. A wire of length l is cut into two parts. One part is bent into a circ...

    Text Solution

    |

  18. A point P is given on the circumference of a circle of radius rdot Cho...

    Text Solution

    |

  19. The circle x^2+y^2=1 cuts the x-axis at Pa n dQdot Another circle with...

    Text Solution

    |

  20. Find the point (alpha,)beta on the ellipse 4x^2+3y^2=12 , in the first...

    Text Solution

    |