Home
Class 12
MATHS
If the slope of the line through the ori...

If the slope of the line through the origin which is tangent to the curve `y=x^(3)+x+10` is `m`, then the value of `m-12` is

Text Solution

Verified by Experts

The correct Answer is:
1
`(dy)/(dx):|_(x_(1),y_(1))=3x_(1)^(2)+1=(y_(1))/(x_(1))`
`3x_(1)^(3)+x_(1)=x_(1)^(3)+x_(1)+16`
`x_(1)=2`, or `y_(1)=26:.m=13`
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

If the slope of line through the origin which is tangent to the curve y=x^(3)+x+16 is m, then the value of m-4 is

If the slope of a line that passes through the origin which is tangent to y= x^(3) + x + 54 is m, then m is equal to

The value of a for which y=27x+ a is a tangent to the curve y=x^(3) are

Slope of the tangent to the curve y=x^(2)+3 at x=2 is

Point at which the tangent to the curve y=3x-2x^(2) has slope m=-1 is

Let l be the line through (0,0) an tangent to the curve y = x^(3)+x+16. Then the slope of l equal to :

The slope of the tangent line to the curve y=x^3-2x+1 at x=1 is

Find the slope of the tangent to the curve y=x^(3)-xquad at x=2

If m is the slope of the tangent to the curve e^(y)=1+x^(2) , then

Slope of tangent of the curve y=x^2+x+1 at x=1 is ___

RESONANCE-TEST PAPERS-MATHEMATICS
  1. If f(x)=(4+x)^(n),"n" epsilonN and f^(r)(0) represents the r^(th) deri...

    Text Solution

    |

  2. Let f(x)=x/(1+x^2) and g(x)=(e^(-x))/(1+[x]) (where [.] denote greates...

    Text Solution

    |

  3. If the derivative of an odd cubic polynomial vanishes at two different...

    Text Solution

    |

  4. If f(x) = { 3 + |x-k|, x leq k; a^2 -2 + sin(x-k)/(x-k), xgtk} has min...

    Text Solution

    |

  5. Find the critical (stationary ) points of the function f(X)=(x^(5))/(2...

    Text Solution

    |

  6. If curve y = 1 - ax^2 and y = x^2 intersect orthogonally then the valu...

    Text Solution

    |

  7. If ST and SN are the lengths of subtangents and subnormals respectivel...

    Text Solution

    |

  8. Find the point on the curve y=x^3-11 x+5 at which the tangent is y"...

    Text Solution

    |

  9. The tangents from (1, 2sqrt2) to the hyperbola 16x^2-25y^2 = 400 inclu...

    Text Solution

    |

  10. Find the rate of change of the volume of a sphere with respect to its ...

    Text Solution

    |

  11. ((2x+3y)/5)+(2f(x)+3f(y))/5 and f^(')(0)=p and f(0)=q. Then f^(")(0) i...

    Text Solution

    |

  12. If the function f(x)=-4e^((1-x)/2)+1+x+(x^2)/2+(x^3)/3a n dg(x)=f^(-1)...

    Text Solution

    |

  13. If f^(x)=-f(x)a n dg(x)=f^(prime)(x)a n d F(x)=(f(x/2))^2+(g(x/2))^2 ...

    Text Solution

    |

  14. The curve y=2e^(2x) intersect the y-axis at an angle cot^(-1)|(8n-4)/3...

    Text Solution

    |

  15. If a , b are two real numbers with a<b , then a real number c can be f...

    Text Solution

    |

  16. If the slope of the line through the origin which is tangent to the cu...

    Text Solution

    |

  17. If the curve C in the x y plane has the equation x^2+x y+y^2=1, then t...

    Text Solution

    |

  18. Let parabolas y=x(c-x) and y=x^(2)+ax+b touch each other at the point ...

    Text Solution

    |

  19. The point on the curve 3y=6x-5x^(3) the normal at which passes through...

    Text Solution

    |

  20. A curve is given by the equations x=sec^2theta,y=cotthetadot If the ta...

    Text Solution

    |