Home
Class 11
MATHS
In the mean value theorem, f(b) - f(a) =...

In the mean value theorem, `f(b) - f(a) = (b-a) f(c ) `, if a= 4, b = 9 and f(x) = ` sqrt(x) ` then the value of c is

A

8

B

1/2

C

6.25

D

4

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • MEAN VALUE THEOREMS

    AAKASH SERIES|Exercise PRACTICE SHEET (EXERCISE-I (LEVEL-II (MORE THAN ONE CORRECT ANSWER TYPE QUESTIONS ) )|2 Videos

  • MEAN VALUE THEOREMS

    AAKASH SERIES|Exercise LECTURE SHEET(EXERCISE-I (MORE THAN ONE CORRECT ANSWER TYPE QUESTIONS)|1 Videos

  • MAXIMA AND MINIMA

    AAKASH SERIES|Exercise ADDITIONAL PRACTICE EXERCISE (LEVEL - II (PRACTICE SHEET )(ADVANCED)) (INTEGER TYPE QUESTIONS)|3 Videos

  • MULTIPLE & SUBMULTIPLE

    AAKASH SERIES|Exercise PRACTICE SHEET (EXERCISE - II) (LEVEL - II) (Linked Comprehension Type Questions)|5 Videos

Similar Questions

Explore conceptually related problems

From mean value theorem, f(b)-f(a) = (b-a)f^(1)(x_(1)), a lt x_(1) lt b if f(x) = ( 1)/( x) then x_(1) =

Verify mean value theorem for the function f(x)=x^(2) on [2,4]

Let f(x)=(arc tanx)^(3)+(arc cotx)^(3) . If the range of f(x) is [a,b) then the value of b/(7a) is

If f(x) = cos x , a = ( - pi )/(2) then the value of 'c' of Rolle's theorem in (a,b)

Using Lagrange's mean value theorem for f(x) =cosx, we get that |cos a - cos b | le

If f(a-x) = f(a+x) and f(b-x)=f(b+x)AA x in R where a, b (a gt b) are constants then the period of f(x) is

if the functions f(x) and phi (x ) are continuous in [a,b] and differentiable in (a,b) , then the value of 'c' for the pair of function f (x) = sqrt(x ) , phi (x) = ( 1)/( sqrt(x)) is

If the domain of the function f(x)=sqrt(3cos^(-1)(4x)-pi) is [a,b], then the value of (4a+64b) is

AAKASH SERIES-MEAN VALUE THEOREMS-PRACTICE SHEET (EXERCISE-I (LEVEL-I))
  1. The value of 'c' prescribed by Lagrange's mean value theorem , when f(...

    Text Solution

    |

  2. The value of C in the lagrange's mean value theroem for f(x) = sqrt( x...

    Text Solution

    |

  3. The value of 'theta' of the Lagrange's mean value theorem for f(x) = x...

    Text Solution

    |

  4. The chord joining the points where x=p and x=q on the curve y =a x^(2)...

    Text Solution

    |

  5. Value of 'c' of Lagrange's mean value theorem for f(x) = 2x - x^(2) i...

    Text Solution

    |

  6. If a lt c lt b , and if 1-k(1) lt ln ((b)/(a)) lt k(2) -1 , then ( ...

    Text Solution

    |

  7. If a(1) lt ( 257)^(1//4) -4 lt b (1), then (a(1) , b(1) ) ( a(1) , b(...

    Text Solution

    |

  8. For the function f(x) = (x-1) ( x-2) ( x-3) in [0,4], value of 'c' in ...

    Text Solution

    |

  9. Let f be a function which is continuous and differentiable for all rea...

    Text Solution

    |

  10. The value of c in Lagrange's Mean Value theorem for the function f(x) ...

    Text Solution

    |

  11. The value of 'c' of Lagrange's mean value theorem for f(x) = x^(3) - 5...

    Text Solution

    |

  12. In the mean value theorem, f(b) - f(a) = (b-a) f(c ) , if a= 4, b = 9 ...

    Text Solution

    |

  13. The constant c of Lagrange's mean value theorem for f(x) =2 sin x+ sin...

    Text Solution

    |

  14. If f(x) = x^(n) for 0 lt a lt b and na^(n-1) le (b^(n) - a^(n))/( b-a...

    Text Solution

    |

  15. Let f(x) and g(x) be differentiable functions in (a,b) continuous in [...

    Text Solution

    |

  16. Lagrange's mean value theorem cannot be applied for

    Text Solution

    |

  17. Let f(x) and g(x) be two differentiable functions in R such that f(2) ...

    Text Solution

    |

  18. If the function f(x) and phi (x) are continuous in [a,b] and different...

    Text Solution

    |

  19. Statement 1 : If 27a+9b+3c+d=0, then the equation f(x) =4ax^(3) + 3b^(...

    Text Solution

    |

  20. Assertion (A) : Suppose f is differentiable on R such that 1le f'(x ) ...

    Text Solution

    |