Home
Class 12
MATHS
If m and n are positive integers and f(x...

If m and n are positive integers and `f(x) = int_1^x(t-a )^(2n) (t-b)^(2m+1) dt , a!=b`, then

A

`x=b` is a point of local minimum

B

`x=b` is a point of local maximum

C

`x=a` is a point of local minimum

D

`x=a` is a point of local maximum

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    VK JAISWAL|Exercise EXERCISE (ONE OR MORE THAN ANSWER IS/ARE CORRECT )|29 Videos
  • APPLICATION OF DERIVATIVES

    VK JAISWAL|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|16 Videos
  • AREA UNDER CURVES

    VK JAISWAL|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|8 Videos

Similar Questions

Explore conceptually related problems

If (x-a)^(2m)(x-b)^(2n+1), where m and n are positive integers and a>b, is the derivative of a function f then-

Let f(x)=int_(1)^(x)(3^(t))/(1+t^(2))dt , where xgt0 , Then

A periodic function with period 1 is integrable over any finite interval.Also,for two real numbers a,b and two unequal non-zero positive integers m and nint_(a)^(a+n)f(x)dx=int_(b)^(b+m)f(x) calculate the value of int_(m)^(n)f(x)dx

If m and n are positive integers, then prove that the coefficients of x^(m) " and " x^(n) are equal in the expansion of (1+x)^(m+n)

Find the points of minima for f(x)=int_(0)^(x)t(t-1)(t-2)dt

If x,y are positive real numbers and m, n are positive integers, then prove that (x^(n) y^(m))/((1 + x^(2n))(1 + y^(2m))) le (1)/(4)

Let T_(r) denote the rth term of a G.P.for r=1,2,3,... If for some positive integers m and n, we have T_(m)=1/n^(2) and T_(n)=1/m^(2) ,then find the value of T_(m+n/2)

If x and y are positive real numbers and m,n are any positive integers,then (x^(n)y^(m))/((1+x^(2n))(1+y^(2m)))<(1)/(4)

VK JAISWAL-APPLICATION OF DERIVATIVES -EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. If m and n are positive integers and f(x) = int1^x(t-a )^(2n) (t-b)^(2...

    Text Solution

    |

  2. A conical vessel is to be prepared out of a circular sheet of metal of...

    Text Solution

    |

  3. On [1,e], then least and greatest vlaues of f (x) = x^(2)ln x are m a...

    Text Solution

    |

  4. If f (x)= (px)/(e ^(x)) - (x ^(2))/(2) + x is a decreasing function f...

    Text Solution

    |

  5. Let f (x)= {{:( xe ^(ax)"," , x le 0),( x+ ax ^(2)-x ^(3)"," , x gt 0)...

    Text Solution

    |

  6. Find sum of all possible values of the real parameter 'b' is the diffe...

    Text Solution

    |

  7. Let 'theta' be the angle in radians between the curves (x ^(2))/(36) +...

    Text Solution

    |

  8. Let set of all possible values of lamda such that f (x)= e ^(2x) - (la...

    Text Solution

    |

  9. Let a,b,c and d be non-negative real number such that a ^(5)+b^(5) le ...

    Text Solution

    |

  10. There is a point (p,q) on the graph of f(x)=x^2 and a point (r , s) on...

    Text Solution

    |

  11. f (x)= max |2 sin y-x| where y in R then determine the minimum value o...

    Text Solution

    |

  12. Let f (x) = int (0)^(x) ((a -1) (t ^(2)+t+1)^(2) -(a+1)(t^(4)+t ^(2) +...

    Text Solution

    |

  13. The numbr of real roots of the equation x ^(2013)+ e ^(20144x) =0 is

    Text Solution

    |

  14. Let the maximum value of expression y= (x ^(4)-x ^(2))/(x ^(6) + 2x ^(...

    Text Solution

    |

  15. The least positive integral value of 'k' for which there exists at lea...

    Text Solution

    |

  16. Let f (x) =x ^(2) +2x -t ^(2) and f(x)=0 has two root alpha (t ) and b...

    Text Solution

    |

  17. A tank contains 100 litres of fresh water. A solution containing 1 gm/...

    Text Solution

    |

  18. If f (x) is continous and differentiable in [3,9) and f'(x) in [-2,8] ...

    Text Solution

    |

  19. It is given that f 9x) is difined on R satisfyinf f (1)=1 and for AA ...

    Text Solution

    |

  20. The number of normals to the curve 3y ^(3) =4x which passes through th...

    Text Solution

    |

  21. Find the number of real root (s) of the equation ae ^(x) =1+ x + (x ^(...

    Text Solution

    |