Home
Class 12
MATHS
Let f(x)=(x-a)^2+(x-b)^2+(x-c)^2dot Then...

Let `f(x)=(x-a)^2+(x-b)^2+(x-c)^2dot` Then, `f(x)` has a minimum at `x=` `(a+b+c)/3` (b) `1/2` (c) `1/8` (d) none of these

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • LINEAR PROGRAMMING

    RD SHARMA ENGLISH|Exercise All Questions|144 Videos

  • MEAN AND VARIANCE OF A RANDOM VARIABLE

    RD SHARMA ENGLISH|Exercise All Questions|125 Videos

Similar Questions

Explore conceptually related problems

Let f(x)=(x-a)^2+(x-b)^2+(x-c)^2 . Then, f(x) has a minimum at x= (a+b+c)/3 (b) 3sqrt(a b c) (c) 3/(1/a+1/b+1/c) (d) none of these

The minimum value of f(x)=x^4-x^2-2x+6 is (a) 6 (b) 4 (c) 8 (d) none of these

Given the function f(x)=x^2e^-(2x) ,x>0. Then f(x) has the maximum value equal to a) e^-1 b) (2e)^-1 . c) e^-2 d) none of these

The function f(x)=x/2+2/x has a local minimum at (a) x=2 (b) x=-2 (c) x=0 (d) x=1

If 2f(x)-3f(1/x)=x^2(x!=0), then f(2) is equal to (a) -7/4("b")""5/2 (c) -1 (d) none of these

If 8f(x)+6f(1/x)=x+5 and y=x^2(f(x), then (dy)/(dx) at x=-1 is equal to (a)0 (b) 1/(14) (c) -1/4 (d) None of these

The function f(x)=e^x+x , being differentiable and one-to-one, has a differentiable inverse f^(-1)(x)dot The value of d/(dx)(f^(-1)) at the point f(log2) is (a) 1/(1n2) (b) 1/3 (c) 1/4 (d) none of these

Let f(x)={(sinx^2)/x x!=0 0x=0, then f^(prime)(0^+)+f^(prime)(0^-) has the value equal to (a) 0 (b) 1 (c) 2 (d) None of these

The function f(x)=e^x+x , being differentiable and one-to-one, has a differentiable inverse f^(-1)(x)dot The value of d/(dx)(f^(-1)) at the point f(log2) is 1/(1n2) (b) 1/3 (c) 1/4 (d) none of these

Let f(x)=(1+x)/(1-x) . If A is matrix for which A^3=0 ,then f(A) is (a) I+A+A^2 (b) I+2A+2A^2 (c) I-A-A^2 (d) none of these

RD SHARMA ENGLISH-MAXIMA AND MINIMA-All Questions
  1. The least value of the function f(x)=x^3-18 x^2+96 x in the interval [...

    Text Solution

    |

  2. The maximum value of x^(1/x),x >0 is (a)e^(1/e) (b) (1/e)^e (c)...

    Text Solution

    |

  3. Let f(x)=(x-a)^2+(x-b)^2+(x-c)^2dot Then, f(x) has a minimum at x= (a...

    Text Solution

    |

  4. Show that of all the rectangles inscribed in a given fixed circle, ...

    Text Solution

    |

  5. AB is a diameter of a circle and C is any point on the circumference o...

    Text Solution

    |

  6. Find the points of local maxima and local minima, if any, y = 3x^3+...

    Text Solution

    |

  7. Find the local maximum and local minimum value of f(x)=secx+logcos^2x...

    Text Solution

    |

  8. Amongst all pairs of positive numbers with product 256, find those ...

    Text Solution

    |

  9. Find two positive numbers whose sum is 14 and the sum of whose squa...

    Text Solution

    |

  10. A beam is supported at the two ends and is uniformly loaded. The ben...

    Text Solution

    |

  11. Show that all the rectangles with a given perimeter, the square has...

    Text Solution

    |

  12. Find all the points of local maxima and local minima of the functio...

    Text Solution

    |

  13. Show that the function f(x)=4x^3-18 x^2+27 x-7 has neither maxima nor ...

    Text Solution

    |

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

    Text Solution

    |

  15. Find all the points of local maxima and minima and the corresponding...

    Text Solution

    |

  16. Find the points of local maxima, local minima and the points of inf...

    Text Solution

    |

  17. Find the point of local maxima or local minima of the function f(x) ...

    Text Solution

    |

  18. Prove that the area of right-angled triangle of given hypotenuse is...

    Text Solution

    |

  19. Show that the total surface area of a closed cuboid with square bas...

    Text Solution

    |

  20. Find the maximum and the minimum values, if any, of the following f...

    Text Solution

    |