Home
Class 12
MATHS
Find the points of local maxima or lo...

Find the points of local maxima or local minima, if any, using first derivative test, and local maximum or local minimum of `f(x)=xsqrt(1-x),\ \ x >0`

Text Solution

AI Generated Solution

To find the points of local maxima or local minima for the function \( f(x) = x \sqrt{1 - x} \) for \( x > 0 \), we will use the first derivative test. Here’s a step-by-step solution: ### Step 1: Find the first derivative \( f'(x) \) Using the product rule, we differentiate \( f(x) \): \[ f'(x) = \frac{d}{dx}(x) \cdot \sqrt{1 - x} + x \cdot \frac{d}{dx}(\sqrt{1 - x}) \] ...
Promotional Banner

Topper's Solved these Questions

  • LINEAR PROGRAMMING

    RD SHARMA|Exercise Solved Examples And Exercises|52 Videos
  • MEAN AND VARIANCE OF A RANDOM VARIABLE

    RD SHARMA|Exercise Solved Examples And Exercises|113 Videos

Similar Questions

Explore conceptually related problems

Find the points of local maxima or local minima,if any,using first derivative test,and local maximum or local minimum of f(x)=(x-5)^(4)

Find the points of local maxima or local minima,if any,using first derivative test,and local maximum or local minimum of ' f(x)=cos x,110

Find the points of local maxima or local minima,if any,using first derivative test,and local maximum or local minimum of f(x)=x^(3)-3x

Find the points of local maxima or local minima,if any,using first derivative test,and local maximum or local minimum of f(x)=sin2x,0

Find the points of local maxima or local minima,if any,using first derivative test,and local maximum or local minimum of f(x)=(x-1)(x+2)^(2)

Find the points of local maxima or local minima,if any,using first derivative test,and local maximum or local minimum of f(x)=x^(3)(x-1)^(2)

Find the points of local maxima or local minima,if any,using first derivative test,and local maximum or local minimum of f(x)=(1)/(x^(2)+2)

Find the points of local maxima or local minima,if any,using first derivative test,and local maximum or local minimum of f(x)=x^(3)(2x-1)^(3)

Find the points of local maxima or local minima,if any,using first derivative test,and local maximum or local minimum of f(x)=x^(3)-6x^(2)+9x+15

Find the points of local maxima or local minima, if any, using first derivative test, and local maximum or local minimum of f(x)=sinx-cosx , 0

RD SHARMA-MAXIMA AND MINIMA-Solved Examples And Exercises
  1. Find the points of local maxima or local minima, if any, using firs...

    Text Solution

    |

  2. Find the points of local maxima or local minima, if any, using firs...

    Text Solution

    |

  3. Find the points of local maxima or local minima, if any, using firs...

    Text Solution

    |

  4. Find the points of local maxima or local minima, if any, using firs...

    Text Solution

    |

  5. Find the points of local maxima or local minima, if any, using firs...

    Text Solution

    |

  6. Find all the points of local maxima and minima and the correspondin...

    Text Solution

    |

  7. Find all the points of local maxima and minima and the correspondin...

    Text Solution

    |

  8. Find the points of local maxima and local minima, if any, and local...

    Text Solution

    |

  9. Find the points of local maxima and local minima, if any, and local...

    Text Solution

    |

  10. Find the points of local maxima and local minima, if any, and local ...

    Text Solution

    |

  11. Find the points of local maxima or local minima, if any, and local m...

    Text Solution

    |

  12. Find the points of local maxima and local minima, if any, and local...

    Text Solution

    |

  13. Find the points of local maxima and local minima, if any, and local ...

    Text Solution

    |

  14. Find the points of local maxima and local minima, if any, and local...

    Text Solution

    |

  15. Find the points of local maxima and local minima, if any, and local...

    Text Solution

    |

  16. Find the local maximum and local minimum values of f(x)=secx+logcos...

    Text Solution

    |

  17. Show that none of the following functions has a local maximum or a ...

    Text Solution

    |

  18. Show that none of the following functions has a local maximum or a ...

    Text Solution

    |

  19. Find the maximum profit that a company can make, if the profit func...

    Text Solution

    |

  20. At what points, the slope of the curve y=-x^3+3x^2+9x-27 at point (...

    Text Solution

    |