Home
Class 12
MATHS
Find all points of local maxima and loca...

Find all points of local maxima and local minima of the function f given by`f(x)=x^3-3x+3`.

Text Solution

AI Generated Solution

To find the local maxima and minima of the function \( f(x) = x^3 - 3x + 3 \), we will follow these steps: ### Step 1: Find the first derivative of the function We start by differentiating the function \( f(x) \) with respect to \( x \). \[ f'(x) = \frac{d}{dx}(x^3 - 3x + 3) \] ...
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    NCERT ENGLISH|Exercise EXERCISE 6.3|27 Videos
  • APPLICATION OF INTEGRALS

    NCERT ENGLISH|Exercise EXERCISE 8.2|7 Videos

Similar Questions

Explore conceptually related problems

Find all the points of local maxima and local minima of the function f given by f(x)=2x^3-6x^2+6x+5 .

Find all the points of local maxima and minima of the function f given by f(x)= 4x^(3)-12x^(2)+12x+10

Find all the points of local maxima and minima of the function f given by f(x)= sinx- cosx , x in [0,2pi]

Find all the points of local maxima and local minima of the function f(x)=x^3-6x^2+12 x-8.

Find all the points of local maxima and local minima of the function f(x)=x^3-6x^2+12 x-8 .

Find the points of local maxima and minima of the function f given by f(x)= x^(3)-12x^(2)+36x+5 .

Find all the points of local maxima and local minima of the function f(x)=(x-1)^3(x+1)^2 (a) 1,-1,-1/5 (b) 1,-1 (c) 1,-1/5 (d) -1,-1/5

Find the points of local maxima and local minima of the function f(x)=2x^(3)-3x^(2)-12x+8 .

Find all the points of local maxima and minima of the function f(x)=x^3-6x^2+9x-8 .

Find the points of local maxima and minima of the function f(x)=x^(2)-4x .

NCERT ENGLISH-APPLICATION OF DERIVATIVES-SOLVED EXAMPLES
  1. Find the maximum and minimum values of f , if any, of the function gi...

    Text Solution

    |

  2. Find the maximum and the minimum values, if any, of the function f gi...

    Text Solution

    |

  3. Find all points of local maxima and local minima of the function f gi...

    Text Solution

    |

  4. Find the maximum and the minimum values, if any, of the function give...

    Text Solution

    |

  5. Let f(x)=3x^(4)+4x^(3)-12x^(2)+12. Find local maximum and minimum valu...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  8. Find local minimum value of the function f given by f(x)=3+|x|,x in R...

    Text Solution

    |

  9. Let AB and CD be two vertical poles at point A and B , respectively ,...

    Text Solution

    |

  10. If the length of three sides of a trapezium other than the base is 1...

    Text Solution

    |

  11. Find two positive numbers whose sum is 15 and the sum of whose square...

    Text Solution

    |

  12. Find the shortest distance of the point (0, c) from the parabola y=x^2...

    Text Solution

    |

  13. Prove that the radius of the right circular cylinder of greatest cu...

    Text Solution

    |

  14. Find the absolute maximum and minimum values of a function f given ...

    Text Solution

    |

  15. Show that the function f(x) = cos x (i) is strictly decreasing funct...

    Text Solution

    |

  16. Prove that the function f given by f(x)=x^3-3x^2+4x is strictly increa...

    Text Solution

    |

  17. Show that the function given by f(x) = 7x-3is strictly increasing on ...

    Text Solution

    |

  18. The total revenue received from the sale of units of a product is...

    Text Solution

    |

  19. The total cost C(x) in Rupees, associated with the production of x u...

    Text Solution

    |

  20. The length x of a rectangle is decreasing at the rate of 3 cm/minute ...

    Text Solution

    |