Home
Class 12
MATHS
The function f(x)=oversetxunderset(-1)in...

The function `f(x)=oversetxunderset(-1)intt(e^t-1)(t-1)(t-2)^3(t-3)^5` dt has a local maximum at x =

A

a)0

B

b)1

C

c)2

D

d)3

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    PATHFINDER|Exercise QUESTION BANK|23 Videos

Similar Questions

Explore conceptually related problems

The function f(x)=underset(-1)overset"x"intt(e^t-1)(t-1)(t-2)^3(t-3)^5 dt has a local minimum at 'x' equal to

The points for which the function f(x)=underset1overset"x"int{2(t-1)(t-2)^3+3(t-1)^2(t-2)^2} dt attins maxima and minima is :

if f(x)oversetxunderseto(int)e^(t^2)(t-2)(t-3)dt for all x in(0,oo) , then

Let f:(0,oo)rarrRR be given by f(x)=oversetxunderset(1/x)inte^((t+1/t))dt/t Then

The function f(x) =int_0^xsqrt(1-t^4) dt is such that

In -4 lt x lt 4 , the function f(x)= int_(-10)^(x) (t^(4)-4)e^(-4t) dt has-

Let f(x)=int_0^xe^t(t-1)(t-2)dt , Then f decreases in the interval

f(x) is polynomial function of degree 6, which satisfies ("lim")_(x_vec_0)(1+(f(x))/(x^3))^(1/x)=e^2 and has local maximum at x=1 and local minimum at x=0a n dx=2. then 5f(3) is equal to

Investigate for maxima and minima of the function f(x) =int_(1)^(x)[2(t-1)(t-2)^(3)+3(t-1)^(2)(t-2)^(2)]dt .

The interval in which f(x) defined by f(x) = int_(-1)^x (t^2+2t)(t^2-1) dt increases

PATHFINDER-APPLICATION OF DERIVATIVE-QUESTION BANK
  1. Using calculus find the order relation between x and tan^(-1) x when "...

    Text Solution

    |

  2. The number of critical points of f(x)=(|x-1|)/X^2 is

    Text Solution

    |

  3. The function f(x)=oversetxunderset(-1)intt(e^t-1)(t-1)(t-2)^3(t-3)^5 d...

    Text Solution

    |

  4. Use the function f(x)=x^(1//x),xgt0 to determine the bigger of the two...

    Text Solution

    |

  5. Show that (x^5-5x^4+5x^3-1) has a local maximum when x = 1, a local mi...

    Text Solution

    |

  6. Find the point on the parabola y^2=2x which is closest to the point (1...

    Text Solution

    |

  7. In a right -angled triangle, prove that r+2R=S.

    Text Solution

    |

  8. Show that the semivertical angle of a cone of maximum volume and of gi...

    Text Solution

    |

  9. Let f(x)={(|x-2|+a^2-9a-9,ifxlt2, 2x-3 ,ifxge2:} Then find value of 'a...

    Text Solution

    |

  10. Find the values of 'm' for which the equation x^4-(m-3)x^2+m=0 has Fo...

    Text Solution

    |

  11. The difference between the greatest and least values of the function f...

    Text Solution

    |

  12. The tangent and normal to the curve y=2sinx+sin2x are drown at P(x=pi/...

    Text Solution

    |

  13. Show that the sum of the intercepts of the tangent to the curve sqrtx+...

    Text Solution

    |

  14. Find the point on the curve y-e^(xy)+x=0. At which we have vertical ta...

    Text Solution

    |

  15. Find the lengths of tangent, subtangent, normal and subnormal to y^2=4...

    Text Solution

    |

  16. If the length of subnormal is equal to length of subtangent at a point...

    Text Solution

    |

  17. Find the angle of intersection between the following curves, y^2=4x an...

    Text Solution

    |

  18. Show that x=y^2 and xy = k cut orthogonally if 8k^2=1

    Text Solution

    |

  19. Show that curves ax^2+by^2=1 and cx^2+dy^2=1 intersect orthogonally if...

    Text Solution

    |

  20. Prove that the curve (x/a)^n+(y/b)^n=2 touches the straught line x/a+y...

    Text Solution

    |