Home
Class 12
MATHS
The function f(x)=x(x+3)e^(-(1/2)x) sati...

The function `f(x)=x(x+3)e^(-(1/2)x)` satisfies the conditions of Rolle's theorem in (-3,0). The value of c, is

A

`-2`

B

`-1`

C

0

D

3

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • 3D COORDINATION SYSTEM

    CENGAGE PUBLICATION|Exercise DPP 3.1|11 Videos
  • APPLICATION OF INTEGRALS

    CENGAGE PUBLICATION|Exercise All Questions|143 Videos

Similar Questions

Explore conceptually related problems

If the function f(x)=4x^(3)+ax^(2)+bx-1 satisfies all the conditions of Rolle's theorem in -(1)/(4) le x le 1 and if f'((1)/(2))=0 , then the values of a and b are -

If the function f(x) stisfies the conditions of Rolle's theorem in [1, 2] and f'(x) is continuous in [1, 2], then int_(1)^(2)f'(x)dx is equal to -

If the function f(x)=a x^3+b x^2+11 x-6 satisfies conditions of Rolles theorem in [1,3] and f'(2+1/(sqrt(3)))=0, then values of a and b , respectively, are

If f(x) satisfies the condition of Rolle's theorem in [1,2] , then int_1^2 f'(x) dx is equal to (a) 1 (b) 3 (c) 0 (d) none of these

If the function f(x) satisfies the condition f(x + 1/x) = x^2 + 1/x^2,x ne 0 then f(x) is

For the function f(x) = e^(cos x) , Rolle's theorem is:

If the function f(x)=x^(3)-ax^(2)+bx-6 defined in 1 le x le 3 satisfies Rolle's theorem when 1lt c lt 3 where c=2+(1)/(sqrt(3)) , find the values of a and b.

If the function f(x)=x^(3)+ax^(2)-bx+4 defined in -2 le x le 2 satisfies Rolle's theorem when -2 lt c lt 2 where c=(1)/(3)(1+sqrt(13)) , then find the values of a and b.

If the function f(x)=x^3-6x^2+a x+b defined on [1,3] satisfies Rolles theorem for c=(2sqrt(3)+1)/(sqrt(3) then find the value of aa n db

Consider the function f(x)=8x^2-7x+5 on the interval [-6,6] .the value of c that satisfies the condition of the mean value theorem is

CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. If there is an error of k % in measuring the edge of a cube, then the ...

    Text Solution

    |

  2. A lamp of negligible height is placed on the ground l1 away from a wal...

    Text Solution

    |

  3. The function f(x)=x(x+3)e^(-(1/2)x) satisfies the conditions of Rolle'...

    Text Solution

    |

  4. The radius of a right circular cylinder increases at the rate of 0.1 ...

    Text Solution

    |

  5. A cube of ice melts without changing its shape at the uniform rate o...

    Text Solution

    |

  6. The radius of the base of a cone is increasing at the rate of 3 cm/min...

    Text Solution

    |

  7. If f(x)=x^3+7x-1, then f(x) has a zero between x=0a n dx=1 . The theor...

    Text Solution

    |

  8. Consider the function f(x)={{:(xsin(pi)/(x),"for"xgt0),(0,"for"x=0):} ...

    Text Solution

    |

  9. Let f(x)a n dg(x) be differentiable for 0lt=xlt=1, such that f(0)=0,g(...

    Text Solution

    |

  10. If 3(a+2c)=4(b+3d), then the equation a x^3+b x^2+c x+d=0 will have (a...

    Text Solution

    |

  11. A value of c for which the conclusion of Mean value theorem holds for ...

    Text Solution

    |

  12. For f(x)=4x^(3)+3x^(2)-x-1, the range of vaues of (f(x(1))-f(x(2)))/(x...

    Text Solution

    |

  13. Let f(x) be a twice differentiable function for all real values of x a...

    Text Solution

    |

  14. The value of c in Largrange's theorem for the function f(x)= log(e) s...

    Text Solution

    |

  15. In which of the following function Rolle's theorem is applicable ?

    Text Solution

    |

  16. Let f^(prime)(x)=e^x^2 and f(0)=10. If A< f(1)< B can be concluded fro...

    Text Solution

    |

  17. If f(x)a n dg(x) are differentiable functions for 0lt=xlt=1 such that ...

    Text Solution

    |

  18. A continuous and differentiable function y=f(x) is such that its graph...

    Text Solution

    |

  19. A man 2m tall, walks at the rate of 1 2/3m//s e c towards a street lig...

    Text Solution

    |

  20. A man 2m tall, walks at the rate of 1 2/3m//s e c towards a street lig...

    Text Solution

    |