Home
Class 12
MATHS
A differentiable function f(x) satisfies...

A differentiable function f(x) satisfies `f(0)=0 and f(1)=sin1`, then (where f' represents derivative of f)

A

`f'(c )=cosc, AA c in[0, 1]`

B

`f'(c )=cosc` for some ` in [0, 1]`

C

`f'(c )=-cos c, AA cin [0, 1]`

D

`f' (c )=2cos c, AA c in [0, 1]`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • NTA JEE MOCK TEST 46

    NTA MOCK TESTS|Exercise MATHEMATICS|25 Videos

  • NTA JEE MOCK TEST 48

    NTA MOCK TESTS|Exercise MATHEMATICS|25 Videos

Similar Questions

Explore conceptually related problems

A differentiable function y=f(x) satisfies f'(x)=(f(x))^(2)+5 and f(0)=1. Then the equation of tangent at the point where the curve crosses y-axis,is

A differential function y=f(x) satisfies f(x)-(f(x))^(2)+5 and f(0)=1. Then the equation of tangent at the point where the curve crosses y-axis is

Let f be two differentiable function satisfying f(1)=1,f(2)=4, f(3)=9 , then

Determine a differentiable function y=f(x) which satisfies f'(x)=[f(x)]^(2) and f(0)=-(1)/(2). Find also the equation of the tangent at the point where the curve crosses the y-axis.

Suppose |[f'(x),f(x)],[f''(x),f'(x)]|=0 is continuously differentiable function with f^(prime)(x)!=0 and satisfies f(0)=1 and f'(0)=2 then (lim)_(x->0)(f(x)-1)/x is 1//2 b. 1 c. 2 d. 0

If f(x) is a differentiable function satisfying |f'(x)|le4AA x in [0, 4] and f(0)=0 , then

NTA MOCK TESTS-NTA JEE MOCK TEST 47-MATHEMATICS
  1. If x=sin(2tan^(-1)3)and y=sin((1)/(2)tan^(-1)(4/3)), then

    Text Solution

    |

  2. A tower subtends an angle of 60^(@) at a point on the same level as th...

    Text Solution

    |

  3. The function f:(-oo, 1] rarr (0, e^(5)] defined as f(x)=e^(x^(3)+2) is

    Text Solution

    |

  4. The function f(x)=lim(nrarroo)((x-2)^(2n)-1)/((x-2)^(2n)+1) (AA n in N...

    Text Solution

    |

  5. If a and b are positive integers such that N=(a+ib)^(3)-107i (where N ...

    Text Solution

    |

  6. The area (in sq. units) bounded by the curve y={{:(x.":",x in ["0, 1"]...

    Text Solution

    |

  7. Let a variable line passing through a fixed point P in the first quadr...

    Text Solution

    |

  8. A differentiable function f(x) satisfies f(0)=0 and f(1)=sin1, then (...

    Text Solution

    |

  9. If I=int(dx)/(x^(3)(x^(8)+1)^(3//4))=(lambda(1+x^(8))^((1)/(4)))/(x^(2...

    Text Solution

    |

  10. The order of the differential equation of the family of parabolas symm...

    Text Solution

    |

  11. The harmonic mean of two positive numbers a and b is 4, their arithmet...

    Text Solution

    |

  12. The shortest distance between the lines (x-2)/(2)=(y-3)/(2)=(z-0)/(1) ...

    Text Solution

    |

  13. If x^(2a)y^(3b)=e^(5m), x^(3c)y^(4d)=e^(2n), Delta(1)=|(5m, 3b),(2n, 4...

    Text Solution

    |

  14. For the equation |x^(2)-2x-3|=b, which of the following statements is ...

    Text Solution

    |

  15. The converse of p rArr (q rArr r) is

    Text Solution

    |

  16. If 4x+3y-12=0 touches (x-p)^(2)+(y-p)^(2)=p^(2), then the sum of all t...

    Text Solution

    |

  17. If A and B are two events such that P(A)=(4)/(7), P(AnnB)=(3)/(28) and...

    Text Solution

    |

  18. If the number of terms free from radicals in the expansion of (7^((1)/...

    Text Solution

    |

  19. Let y=sqrt(xlog(e)x). If the value of (dy)/(dx) at x=e^(4) is k, then ...

    Text Solution

    |

  20. If the value of the integral I=int((pi)/(4))^((pi)/(3))" max "(sinx, t...

    Text Solution

    |