Home
Class 12
MATHS
Let f(x+y)=f(x)*f(y)AAx , y in R,suppo...

Let `f(x+y)=f(x)*f(y)AAx , y in R`,suppose that `f(3)=3 and f^(prime)(0)=11` , then `f'(3)` is given by

A

22

B

44

C

28

D

33

Text Solution

Verified by Experts

The correct Answer is:
D
`f'(3)=underset(xto0)lim(f(3+h)-f(3))/(h)`
`=underset(xto0)lim(f(3)*f(h)-f(3))/(h)`
`impliesf'(3)=3underset(x to 0)lim(f(h)-1)/(h)" "[becausef(3)=3]`
Use L'Hospital rule,
`impliesf'(3)=3underset(hto0)lim(f'(h))/(1)`
`=3f'(0)" "[becausef'(0)=11]`
`=3xx11=33`
Promotional Banner

Topper's Solved these Questions

  • MHTCET 2010

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise Mathematics|50 Videos

  • MHTCET 2012

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MATHEMATICS|50 Videos

Similar Questions

Explore conceptually related problems

Let f(x+y)=f(x)*f(y)AA x,y in R suppose that f(3)=3 and f'(0)=11 then f'(3) is given by

Let f(x+y)=f(x)f(y) for all x,y in R suppose that f(3)=3,f(0)!=0 and f'(0)=11, then f'(3) is equal

Let f(x + y) = f(x) .f(y) AA x, y in R suppose that f(k) =3, k in R and f'(0) = 11 then find f'(k)

Let f(x+y)=f(x)f(y) for all x and y . Suppose f(5)=2 and f^(prime)(0)=3 , find f^(prime)(5) .

If f((x+2y)/3)=(f(x)+2f(y))/3\ AA\ x ,\ y in R and f^(prime)(0)=1 , f(0)=2 , then find f(x) .

Let f(x+y)+f(x-y)=2f(x)f(y)AA x,y in R and f(0)=k, then

Let f(x+y)=f(x).f(y) for all x and y suppose f(5)=2 and f'(0)=3. Find f'(5) .

If f(x+y)=f(x)+f(y),AAx ,\ y in R then prove that f(k x)=kf(x)for\ AAk ,\ x in Rdot

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-MHTCET 2011-METHEMATICS
  1. If f(x)=e^(x)g(x),g(0)=2,g'(0)=1, then f'(0) is

    Text Solution

    |

  2. If a, b, c and d are positive then lim(x to oo)(1+(1)/(a+bx))^(x+dx) ...

    Text Solution

    |

  3. Let f(x+y)=f(x)*f(y)AAx , y in R,suppose that f(3)=3 and f^(prime)(0...

    Text Solution

    |

  4. If G(x)=-sqrt(25-x^(2)),then lim(xto1) (G(x)-G(t))/(x-1) is

    Text Solution

    |

  5. At the point x = 1 , then function f(x) = {{:(x^(3) - 1, 1lt x lt o...

    Text Solution

    |

  6. If x^(p) y^(q) = (x + y)^((p + q)) " then " (dy)/(dx)= ?

    Text Solution

    |

  7. If x = 2 cos t - cos 2t , y = 2 sin t - sin 2t, then the value of ...

    Text Solution

    |

  8. y=logtan(x/2)+sin^(-1)(cosx), then dy/dx is

    Text Solution

    |

  9. The minimum value of (1-x+x^2)/(1+x+x^2) for all real values ​​of x is...

    Text Solution

    |

  10. If x+y=k is normal to y^2=12 x , then k is 3 (b) 9 (c) -9 (d) -3

    Text Solution

    |

  11. A particle moves along a straight line according to the law s=16-2t+3t...

    Text Solution

    |

  12. Find: int[sqrt(cotx)+sqrt(tan x)]dx

    Text Solution

    |

  13. int(x^(2))/((x sinx+cosx)^(2))dx is equal to

    Text Solution

    |

  14. Evaluate int(0)^(pi)(x dx)/(1+cos alpha sin x),where 0lt alpha lt pi.

    Text Solution

    |

  15. int(pi//2)^(pi//2)(cosx)/(1+e^(x))dx is equal to

    Text Solution

    |

  16. int(0)^(pi//2)(1)/((1+tanx))dx=?

    Text Solution

    |

  17. The area bounded by the parabola y^2 = x, straight line y = 4 and y-ax...

    Text Solution

    |

  18. Find the differential equation of all the circles which pass throug...

    Text Solution

    |

  19. If m and n are order and degree of the differential equation ((d^2y)/(...

    Text Solution

    |

  20. The integrating factor of the differential equation (dy)/(dx)(x(log)...

    Text Solution

    |