Home
Class 12
MATHS
The length x of a rectangle is decreasin...

The length x of a rectangle is decreasing at the rate of 3 cm/minute and the width y is increasing at the rate of 2cm/minute. When `x =10`cm and `y = 6`cm, find the rates of change of (a) the perimeter and (b) the area of the rectangle.

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    NCERT GUJARATI|Exercise EXERCISE 6.1|18 Videos
  • APPLICATION OF DERIVATIVES

    NCERT GUJARATI|Exercise EXERCISE 6.2|23 Videos
  • APPLICATION OF INTEGRALS

    NCERT GUJARATI|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

The length x of a rectangle is decreasing at the rate of 5 cm/minute and the width y is increasing at the rate of 4 cm/minute. When x = 8 cm and y = 6 cm, find the rates of change of (a) the [erimeter, and (b) the area of the rectangle.

The radius of the cone is increasing at the rate of 4 cm/se. Its height is decreasing at the rate of 3 cm/se. When its radius is 3 cm and height is 4 cm. Find the rate of change of its curved surface area.

The area of a triangle is increasing at the rate of 4 cm^(2)//s . Its altitude is increasing at the rate of 2 cm/s. When the length of its altitude is 20 cm and its area is 30 cm^(2) , find the rate of change of its base.

The radius of a circle is increasing at the rate of 0.7 cm/s. What is the rate of increase of its circumference ?

The side of a square is increasing at the rate of 0.2 cm/s. The rate of increase of perimeter w.r.t time is :

The side of a square is increasing at ther rate of 0.2 cm//s . The rate of increase of perimeter w.r.t. time is :

The volume of a cube is increasing at the rate of 8 cm^(3)//s . How fast is the surface area increasing when the length of an edge is 12 cm ?

An edge of a variable cube is increasing at the rate of 10 cm/s. How fast the volume of the cube is increasing when the edge is 5 cm long?

The radius of a circle is increasing uniformly at the rate of 3 cm/s. Find the rate at which the area of the circle is increasing when the radius is 10 cm.

NCERT GUJARATI-APPLICATION OF DERIVATIVES-EXERCISE 6.6
  1. The length x of a rectangle is decreasing at the rate of 3 cm/minute ...

    Text Solution

    |

  2. Using differentials, find the approximate value of each of the followi...

    Text Solution

    |

  3. Show that the function given by f(x)=(logx)/xhas maximum at x = e.

    Text Solution

    |

  4. The two equal sides of an isosceles triangle with fixed base b are ...

    Text Solution

    |

  5. Find the equation of the normal to curve x^2=4ywhich passes through t...

    Text Solution

    |

  6. Show that the normal at any point theta to the curve x=acostheta+at...

    Text Solution

    |

  7. Find the intervals in which the function f given by f(x)=(4sinx-2x-x c...

    Text Solution

    |

  8. Find the intervals in which the function f given by f(x)=\ x^3+1/(...

    Text Solution

    |

  9. Find the maximum area of an isosceles triangle inscribed in the ellip...

    Text Solution

    |

  10. A tank with rectangular base and rectangular sides, open at the top...

    Text Solution

    |

  11. The sum of the perimeter of a circle and square is k, where k is so...

    Text Solution

    |

  12. A window is in the form of a rectangle surmounted by a semicircular...

    Text Solution

    |

  13. A point on the hypotenuse of a triangle is at distance a and b from t...

    Text Solution

    |

  14. Find the points at which the function f given by f(x)=(x-2)^4(x+1)^3 h...

    Text Solution

    |

  15. Find the absolute maximum and minimum values of the function f give...

    Text Solution

    |

  16. Show that the altitude of the right circular cone of maximum volume...

    Text Solution

    |

  17. Let f be a function defined on [a, b] such that f^(prime)(x)>0, for al...

    Text Solution

    |

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

    Text Solution

    |

  19. Show that height of the cylinder of greatest volume which can be insc...

    Text Solution

    |

  20. A cylindrical tank of radius 10 m is being filled with wheat at the r...

    Text Solution

    |

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

    Text Solution

    |