Home
Class 12
MATHS
The least positive integral value of 'k'...

The least positive integral value of `'k'` for which there exists at least one line that the tangent to the graph of the curve `y=x^(3)-kx` at one point and normal to the graph at another point is

Text Solution

Verified by Experts

The correct Answer is:
12
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (MATHCING TYPE PROBLEMS)|6 Videos

  • AREA UNDER CURVES

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise AXERCISE (SUBJECTIVE TYPE PROBLEMS)|8 Videos

Similar Questions

Explore conceptually related problems

Number of positive integral value(s) of a for which the curve y=a^(x) intersects the line y=x is:

The least integral value of 'k' for which (k -2)x^2 +8x+k+4>0 for all xepsilonR , is:

Does there exists line/lines which is/are tangent to the curve y=sinx at (x_1, y_1) and normal to the curve at (x_2, y_2)?

Does there exists line/lines which is/are tangent to the curve y=sinx \ a t(x_1, y_1) and normal to the curve at (x_2, y_2)?

Find the number of positive integral values of k for which kx ^(2) +(k-3)x+1 lt 0 for atleast one positive x.

The set of real values of 'a' for which at least one tangent to y^(2)=4ax becomes normal to the circle x^(2)+y^(2)-2ax-4ay+3a^(2)-0, is

Find the equations of the tangent and the normal to the curve y=x^2+4x+1 at x=3 at the indicated points

Find the equations of the tangent and the normal to the curve y=2x^2-3x-1 at (1,\ -2) at the indicated points

The slope of the tangent to the curve y=x^(2) -x at the point where the line y = 2 cuts the curve in the first quadrant, is

Find the value of k for which the point (1,\ -2) lies on the graph of the linear equation x-2y+k=0

VIKAS GUPTA (BLACK BOOK) ENGLISH-APPLICATION OF DERIVATIVES -EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. If f (x)= (px)/(e ^(x)) - (x ^(2))/(2) + x is a decreasing function f...

    Text Solution

    |

  2. L e tf(x)={x e^(a x),xlt=0x+a x^2-x^3,x >0 where a is a positive cons...

    Text Solution

    |

  3. Find sum of all possible values of the real parameter 'b' if the diffe...

    Text Solution

    |

  4. Let 'theta' be the angle in radians between the curves (x ^(2))/(36) +...

    Text Solution

    |

  5. Let set of all possible values of lamda such that f (x)= e ^(2x) - (la...

    Text Solution

    |

  6. Let a,b,c and d be non-negative real number such that a ^(5)+b^(5) le ...

    Text Solution

    |

  7. There is a point (p,q) on the graph of f(x)=x^(2) and a point (r,s) on...

    Text Solution

    |

  8. If f(x)=max| 2 siny-x|, (where y in R), then find the minimum value o...

    Text Solution

    |

  9. Let f (x) = int (0)^(x) ((a -1) (t ^(2)+t+1)^(2) -(a+1)(t^(4)+t ^(2) +...

    Text Solution

    |

  10. The numbr of real roots of the equation x ^(2013)+ e ^(2014x) =0 is

    Text Solution

    |

  11. Let the maximum value of expression y= (x ^(4)-x ^(2))/(x ^(6) + 2x ^(...

    Text Solution

    |

  12. The least positive integral value of 'k' for which there exists at lea...

    Text Solution

    |

  13. The coordinates of a particle moving in a plane are given by x (t) = a...

    Text Solution

    |

  14. A tank contains 100 litres of fresh water. A solution containing 1 gm/...

    Text Solution

    |

  15. If f (x) is continous and differentiable in [-3,9] and f'(x) in [-2,8]...

    Text Solution

    |

  16. It is given that f (x) is defined on R satisfying f (1)=1 and for AA ...

    Text Solution

    |

  17. The number of normals to the curve 3y ^(3) =4x which passes through th...

    Text Solution

    |

  18. Find the number of real root (s) of the equation ae ^(x) =1+ x + (x ^(...

    Text Solution

    |

  19. Let f (x) = ax+cos 2x +sin x+ cos x is defined for AA x in R and a in...

    Text Solution

    |

  20. If p (1) and p(2) are the lengths of the perpendiculars from origin on...

    Text Solution

    |