Home
Class 12
MATHS
Prove theat the tangent drawn at any poi...

Prove theat the tangent drawn at any point to the curve `f(x)=x^(5)+3x^(3)+4x+8` would make an acute angle with the x-axis.

Promotional Banner

Topper's Solved these Questions

  • 3D COORDINATION SYSTEM

    CENGAGE PUBLICATION|Exercise DPP 3.1|11 Videos

  • APPLICATION OF INTEGRALS

    CENGAGE PUBLICATION|Exercise All Questions|143 Videos

Similar Questions

Explore conceptually related problems

Find the point on the curve y^2=a x the tangent at which makes an angle of 45^0 with the x-axis.

A tangent is drawn to the curve x^(2)(x-y)+a^(2)(x+y)=0 at the origin. Find the angle it makes with the x-axis.

The point on the curve y^(2)=x , the tangent at which makes an angle 45^(@) with the x- axis is-

If the normal at any point to the curve x^((2)/(3))+y^((2)/(3))=a^((2)/(3)) makes an angle phi with the x-axis, then prove that the equation of the normal is ycosphi-xsinphi=acos2phi .

Find the equation of the normal at the points on the curve y=(x)/(1-x^(2)) , where the tangent makes an angle 45^(@) with the axis of x.

Find the points on the curve x^(2) + y^(2) – 2x – 3 = 0 at which the tangents are parallel to the x-axis.

The tangent drawn at the point (0, 1) on the curve y=e^(2x) meets the x-axis at the point -

If the normal at any point to the curve x^(2//3)+y^(2//3)=a^(2//3) makes an angle phi with the x-axis then prove that the equation of the normal is y cos phi- x sin phi = a cos 2phi .

Find points at which the tangent to the curve y = x^(3) – 3x^(2) – 9x + 7 is parallel to the x-axis.

Find the length of tangent to the curve y=4x^3-2x^5 at (-1,1)

CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. The ratio of capitals of three persons is 1:2:3 and the profit of 2nd ...

    Text Solution

    |

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

    Text Solution

    |

  3. Prove theat the tangent drawn at any point to the curve f(x)=x^(5)+3x^...

    Text Solution

    |

  4. Show that height of the cylinder of greatest volume which can be ins...

    Text Solution

    |

  5. A curve is defined parametrically by the the equation x=t^(2) and y=t^...

    Text Solution

    |

  6. The equation of the tangent to the curve y={(x^2sin"1/x,xne0),(0,x=0):...

    Text Solution

    |

  7. Show that the height of the cylinder of maximum volume that can be ...

    Text Solution

    |

  8. Statement 1: If f(x) is differentiable in [0,1] such that f(0)=f(...

    Text Solution

    |

  9. Find the equation of tangent to the curve y=sin^(-1)((2x)/(1+x^2)) a t...

    Text Solution

    |

  10. The lateral surface area of a cube is 169sq.cm., then the volume of th...

    Text Solution

    |

  11. Consider the polynomial function f(x)=x^7/7-x^6/6+x^5/5-x^4/4+x^3/3-x^...

    Text Solution

    |

  12. Find the equations of the normal to the curve y=x^3+2x+6 which are par...

    Text Solution

    |

  13. A sheet of area 40m^2 is used to make an open tank with square base. F...

    Text Solution

    |

  14. Let y=f(x) be a polynomial of odd degree (geq3) with real coefficients...

    Text Solution

    |

  15. Find the equation of tangent and normal to the curve x=(2a t^2)/((1+t^...

    Text Solution

    |

  16. Find the points on the curve 5x^2-8x y+5y^2=4 whose distance from the ...

    Text Solution

    |

  17. If d is the minimum distance between the curves f(x)=e^x a n dg(x)=(l...

    Text Solution

    |

  18. L L ' is the latus rectum of the parabola y^2= 4ax and PP' is a doubl...

    Text Solution

    |

  19. Let f(x0 be a non-constant thrice differentiable function defined on (...

    Text Solution

    |

  20. The tangent to the parabola y=x^2 has been drawn so that the abscissa ...

    Text Solution

    |