Home
Class 12
MATHS
Let f be arry continuously differentiabl...

Let `f` be arry continuously differentiable function on `[a,b]` and twice differentiable on `(a.b)` such that `f(a)=f(a)=0 and f(b)=0.` Then

A

`f''(a) =0`

B

`f '(x) =0` for some `x in (a,b)`

C

`f''(x)=0` for some ` x in (a,b)`

D

`f'''(x) =0` for some `x in (a,b)`

Text Solution

Verified by Experts

The correct Answer is:
B, C
Promotional Banner

Topper's Solved these Questions

  • DERIVATIVES

    MTG-WBJEE|Exercise WB JEE PREVIOUS YEARS QUESTIONS|22 Videos

  • DEFINITE INTEGRALS

    MTG-WBJEE|Exercise WE JEE PREVIOUS YEARS QUESTIONS (CATEGORY 3 : ONE OR MORE THAN ONE OPTION CORRECT TYPE)|5 Videos

  • DIFFERENTIAL EQUATIONS

    MTG-WBJEE|Exercise WB JEE Previous Years Questions|19 Videos

Similar Questions

Explore conceptually related problems

If f(x) is a twice differentiable function such that f(0)=f(1)=f(2)=0 . Then

Let f be any continuous function on [0, 2] and twice differentiable on (0, 2). If f(0) = 0, f(1) = 1 and f(2) = 2, then :

Tet f be continuous on [a,b] and differentiable on (a,b). If f(a)=a and f(b)=b, then

To illustrate the Mean Value Theorem with a specific function, let’s consider f(x) = x^(3) – x, a= 0, b = 2 . since f is a polynomial, it is continuous and differentiable for x, so it is certainly continuous on [0, 2] and differentiable on (0, 2) such that f(2) – f(0) = f'(c)(2 – 0)

Let f:[a,b]rarr R be a function,continuous on [a,b] and twice differentiable on (a,b). If,f(a)=f(b) and f'(a)=f'(b), then consider the equation f''(x)-lambda(f'(x))^(2)=0. For any real lambda the equation hasatleast M roots where 3M+1 is

Let f(x) be a non-constant twice differentiable function defined on (oo,oo) such that f(x)=f(1-x) and f'(1/4)=0^(@). Then

For all twice differentiable functions f : R to R , with f(0) = f(1) = f'(0) = 0

If f be a continuous function on [0,1], differentiable in (0,1) such that f(1)=0, then there exists some c in(0,1) such that

If f be a continuous function on [0,1] differentiable in (0,1) such that f(1)=0, then there exists some c in(0,1) such that

MTG-WBJEE-DERIVATIVES -WB JEE PREVIOUS YEARS QUESTIONS
  1. Let R be the set of all real number and f: [-1,1] to R is difined by ...

    Text Solution

    |

  2. Suppose that f (x) is a differentiable function such that f'(x) is con...

    Text Solution

    |

  3. For all real values of a (0) , a (1), a (2), a (3) satisfying a (0)+ (...

    Text Solution

    |

  4. If y=(1+x)(1+x^2)(1+x^4)(1+x^(2n)), then find (dy)/(dx)a tx=0.

    Text Solution

    |

  5. If y=f(x) is an odd differentiable function defined on (-oo,oo) such ...

    Text Solution

    |

  6. If f (x) = tan ^(-1) [ (log ((e )/( x ^(2))))/(log (ex ^(2)))] + tan ^...

    Text Solution

    |

  7. Consider the non-constant differentiable function f of one variable wh...

    Text Solution

    |

  8. if f(x)=log5 log3 x then f'(e) is equal to

    Text Solution

    |

  9. Let F (x) = e ^(x) , G (x) =e ^(-x) and H (x) = G (F(x)), where x is a...

    Text Solution

    |

  10. IF y = e ^(m sin ^(-1)x)) and (1- x ^(2)) (d ^(2) y )/( dx ^(2)) - x ...

    Text Solution

    |

  11. Let f (x) = {{:((x ^(p))/(( sin x ) ^(q) )"," , 0 lt x le (pi)/(2) ), ...

    Text Solution

    |

  12. For all twice differentiable functions f : R to R , with f(0) = f...

    Text Solution

    |

  13. Let f1(x)=e^x,f2(x)=e^(f1(x)),......,f(n+1)(x)=e^(fn(x)) for all n>=1....

    Text Solution

    |

  14. Let f : [a,b] to Rbe differentiable on [a,b]& k in R. Let f (a) =0 = f...

    Text Solution

    |

  15. Let f (x) gt 0 for all x and f'(x) exists for all x. If f is the inver...

    Text Solution

    |

  16. Applying Largrange's mean value theorem for a suitable function f (x) ...

    Text Solution

    |

  17. The number of points at which the function f(x) = max{a - x, a + x, b}...

    Text Solution

    |

  18. Let f be arry continuously differentiable function on [a,b] and twice ...

    Text Solution

    |

  19. If f(x)=x^n, n being a non-negative integer,then the values of n for...

    Text Solution

    |

  20. Let f: [1,3] to R be a continuous function that is differentiable in (...

    Text Solution

    |