Home
Class 12
MATHS
if f(x)oversetxunderseto(int)e^(t^2)(t-2...

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

A

f has a local maxmimum at x=2

B

f is decreasing on (2,3)

C

there exists some `c in(0,oo)` such that `f''(c)=0`

D

f has a localminimum at x=3

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
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)=oversetxunderset(-1)intt(e^t-1)(t-1)(t-2)^3(t-3)^5 dt has a local maximum at x =

Let f(x)=(1-x)^2sin^2x+x^2 for all xinR and let g(x)=int_1^x((2(t-1))/(t+1)-Int) f(t)dt for all xin(1,oo) Which of the following is true ?

Let f(x)=(1-x)^(2) sin^(2) x+x^(2) for all x in RR , and let g(x)=int_(1)^(x) ((2(t-1))/(t+1)-log t)f(t) dt for all x in (1, oo) . The number of real roots of the equation f(x)=1 in the interval [0, 1] is -

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

Let f(x)=(1-x)^(2) sin^(2) x+x^(2) for all x in RR , and let g(x)=int_(1)^(x) ((2(t-1))/(t+1)-log t)f(t) dt for all x in (1, oo) . Which of the following is true?

Let f(x)=(1-x)^(2) sin^(2) x+x^(2) for all x in RR , and let g(x)=int_(1)^(x) ((2(t-1))/(t+1)-log t)f(t) dt for all x in (1, oo) . Consider the statements : P : there exists some x in RR such that f(x)+2x=2(1+x^(2)) Q : There exists some x in RR such that 2f(x)+1=2x(1+x) then-

If f(x) is a differentiable function in the interval (0, oo) such that f(1)=1 and underset(t to x)lim(t^(2)f(x)-x^(2)f(t))/(t-x)=1 , for each x gt 0 then f((3)/(2)) is equal to

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

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 :

PATHFINDER-APPLICATION OF DERIVATIVE-QUESTION BANK
  1. If y=sec(tan^(-1)x), then value of dy/dx at x=1 is

    Text Solution

    |

  2. If f(x)=e^x(x-2)^2 then

    Text Solution

    |

  3. Let f(x)=sinx+2cos^2x,pi/4lexle(3pi)/4. then f attains its

    Text Solution

    |

  4. Let exp(x) denote exponential function e^x. If f(x)=exp(x^(1/x)).xgt0 ...

    Text Solution

    |

  5. The minimum value of the function f(x)=2|x-1|+|x-2| is

    Text Solution

    |

  6. Let f(x)={(x^2|cos"pi/x|,xne0),(0,x=0):}

    Text Solution

    |

  7. The function f:[0,3]rarr[1,29], defined by f(x)=2x^3-15x^2+36x+1 is

    Text Solution

    |

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

    Text Solution

    |

  9. Let f:IRrarrIR be defined as f(x)=|x|+|x^2-1|.The total number of poin...

    Text Solution

    |

  10. Let p(x) be a real polynomial of least degree which has a local maximu...

    Text Solution

    |

  11. xx

    Text Solution

    |

  12. Let f(x)=(1-x)^2sin^2x+x^2 for all xinR and let g(x)=int1^x((2(t-1))/(...

    Text Solution

    |

  13. A spherical balloon is filled with 4500 pi cubic meters of helium gas....

    Text Solution

    |

  14. Let a, binR be such that the function f given by f(x)=ln|x|+bx^2+ax,xn...

    Text Solution

    |

  15. If f is a real-valued differentiable function such that f(x) f'(x)lt0 ...

    Text Solution

    |

  16. Rolle’s theorem is applicable in the interval [-2, 2] for the function

    Text Solution

    |

  17. Let y=((3^x-1)/(3^x+1))sinx+loge(2+x),xgt-1. Then at x=0 dy/dx equals

    Text Solution

    |

  18. Maximum value of the function f(x)=x/8+2/x on the interval [1,6] is

    Text Solution

    |

  19. For -pi/2ltxlt(3pi)/2, the value of d/dx{tan^(-1)"cosx/(1+sinx)} is eq...

    Text Solution

    |

  20. If f(x) and g(x) are twice differentiable functions on (0,3) satisfyin...

    Text Solution

    |