Home
Class 12
MATHS
The point(s) on the curve y^3+\ 3x^2=1...

The point(s) on the curve `y^3+\ 3x^2=12 y` where the tangent is vertical, is(are) ? (a)`(+-4/(sqrt(3)),\ -2)` (b) `(+-\ sqrt((11)/3,\ )\ 1)` (c)`(0,\ 0)` (d) `(+-4/(sqrt(3)),\ 2)`

A

`(pm 4 sqrt(3),-2)`

B

`(pmsqrt((11)/(3)),1 )`

C

(0,0)

D

`(pm(4)/(sqrt(3)),2)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    AAKASH INSTITUTE ENGLISH|Exercise Assignment SECTION-C( Objective Type Questions ( More than one option are correct ))|1 Videos

  • APPLICATION OF DERIVATIVES

    AAKASH INSTITUTE ENGLISH|Exercise Assignment SECTION-C( Objective Type Questions ( More than one option is correct ))|5 Videos

  • APPLICATION OF DERIVATIVES

    AAKASH INSTITUTE ENGLISH|Exercise Assignment SECTION-A (Competition Level Questions)|50 Videos

  • APPLICATION OF INTEGRALS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment Section - I Aakash Challengers Questions|2 Videos

Similar Questions

Explore conceptually related problems

The point on the curve y=x^2-3x+2 where tangent is perpendicular to y=x is (a) (0,2) (b) (1,\ 0) (c) (-1,\ 6) (d) (2,\ -2)

Points on the curve f(x)=x/(1-x^2) where the tangent is inclined at an angle of pi/4 to the x-axis are (a) (0,0) (b) (sqrt(3),-(sqrt(3))/2) (c) (-2,2/3) (d) (-sqrt(3),(sqrt(3))/2)

Find a point on the curve y=(x-3)^2 , where the tangent is parallel to the line joining (4,\ 1) and (3,\ 0) .

Points on the curve f(x)=x/(1-x^2) where the tangent is inclined at an angle of pi/4 to the x-axis are (0,0) (b) (sqrt(3),-(sqrt(3))/2) (-2,2/3) (d) (-sqrt(3),(sqrt(3))/2)

The incenter of the triangle with vertices (1,sqrt(3)),(0,0), and (2,0) is (a) (1,(sqrt(3))/2) (b) (2/3,1/(sqrt(3))) (c) (2/3,(sqrt(3))/2) (d) (1,1/(sqrt(3)))

If at each point of the curve y=x^3-a x^2+x+1, the tangent is inclined at an acute angle with the positive direction of the x-axis, then (a) a >0 (b) a<-sqrt(3) (c) -sqrt(3)< a< sqrt(3) (d) non eoft h e s e

Number of different points on the curve y^2=x(x+1)^2 where the tangent to the curve drawn at (1,2) meets the curve, is 0 b. 1 c. 2 d. 3

Tangent of acute angle between the curves y=|x^2-1| and y=sqrt(7-x^2) at their points of intersection is (a) (5sqrt(3))/2 (b) (3sqrt(5))/2 (5sqrt(3))/4 (d) (3sqrt(5))/4

A is a point on either of two lines y+sqrt(3)|x|=2 at a distance of 4sqrt(3) units from their point of intersection. The coordinates of the foot of perpendicular from A on the bisector of the angle between them are (a) (-2/(sqrt(3)),2) (b) (0,0) (c) (2/(sqrt(3)),2) (d) (0,4)

The length of the tangent of the curve y=x^(2)+1 at (1 ,3) is (A) sqrt(5) (B) 3sqrt(5) (C) 1/2 (D) 3(sqrt(5))/(2)

AAKASH INSTITUTE ENGLISH-APPLICATION OF DERIVATIVES-Assignment SECTION-B( Objective Type Questions ( One option is correct ))
  1. The sum of the intercepts made on the axes of coordinates by any tange...

    Text Solution

    |

  2. The slope of the tangent to the curve x=t^2+3t-8,\ \ y=2t^2-2t-5 at ...

    Text Solution

    |

  3. The point(s) on the curve y^3+\ 3x^2=12 y where the tangent is ver...

    Text Solution

    |

  4. If f(x)=x^3+4x^2+lambdax+1 is a monotonically decreasing function of x...

    Text Solution

    |

  5. If a function f(x) increases in the interval (a, b). then the function...

    Text Solution

    |

  6. The function f, defined by f(x)=(x^(2))/(2) +In x - 2 cos x increas...

    Text Solution

    |

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

    Text Solution

    |

  8. Which of the following is correct ?

    Text Solution

    |

  9. Find the value of a, if the equation x-sinx=a has a unique root ...

    Text Solution

    |

  10. Number of real roots of the equation e^(x-1)-x=0 is

    Text Solution

    |

  11. If f(x)=x/(sinx) \ a n d \ g(x)=x/(tanx),w h e r e \ 0ltxlt=1, then in...

    Text Solution

    |

  12. If f(x)=(p^2-1)/(p^2+1) x^3-3x + log 2 is a decreasing function of x.i...

    Text Solution

    |

  13. Let f(x)=(x-a)^2+(x-b)^2+(x-c)^2dot Then, f(x) has a minimum at x= (a...

    Text Solution

    |

  14. The maximum value of ((1)/(x))^(2x^(2)) is

    Text Solution

    |

  15. 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

    |

  16. If x in [-1,1] then the minimum value of f(x)=x^(2)+x+1 is

    Text Solution

    |

  17. If ax+(b)/(x) ge c, AA a gt 0 and a,b,c are positive constant then

    Text Solution

    |

  18. The number which exceeds its square by the greatest possible quanti...

    Text Solution

    |

  19. The point (0,3) is nearest to the curve x^(2)=2y at

    Text Solution

    |

  20. Let f(x) be a function defined as follows: f(x)=sin(x^2-3x),xlt=0; a n...

    Text Solution

    |