Home
Class 12
MATHS
Let f (x+y) =f (x) f (y) for all x and y...

Let `f (x+y) =f (x) f (y)` for all x and y, `and f(5)=2, f'(0)=3,` then `f '(5)` is equal to:

A

3

B

1

C

`-6`

D

6

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION

    VK JAISWAL ENGLISH|Exercise EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)|35 Videos
  • CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION

    VK JAISWAL ENGLISH|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|29 Videos
  • COMPOUND ANGLES

    VK JAISWAL ENGLISH|Exercise Exercise-5 : Subjective Type Problems|31 Videos
  • DETERMINANTS

    VK JAISWAL ENGLISH|Exercise EXERCISE-4 : SUBJECTIVE TYPE PROBLEMS|12 Videos

Similar Questions

Explore conceptually related problems

If f(x+y)=f(x) xx f(y) for all x,y in R and f(5)=2, f'(0)=3, then f'(5)=

Let f(x) be a differentiable function on x in R such that f(x+y)=f(x). F(y)" for all, "x,y . If f(0) ne 0, f(5)=12 and f'(0)=16 , then f'(5) is equal to

Let f:RtoR be a function given by f(x+y)=f(x)f(y) for all x,y in R .If f'(0)=2 then f(x) is equal to

If f(x+y)=2f(x) f(y) for all x,y where f'(0)=3 and f(4)=2, then f'(4) is equal to

Let f (x + y) = f(x) f(y) for all x, y, in R , suppose that f(3) = 3 and f '(0) = 2 then f '(3) is equal to-

Let f be a differential function satisfying the condition. f((x)/(y))=(f(x))/(f(y))"for all "x,y ( ne 0) in R"and f(y) ne 0 If f'(1)=2 , then f'(x) is equal to

Let f be a function satisfying f(x+y)=f(x) + f(y) for all x,y in R . If f (1)= k then f(n), n in N is equal to

Let f(x+y) = f(x) + f(y) - 2xy - 1 for all x and y. If f'(0) exists and f'(0) = - sin alpha , then f{f'(0)} is

Let f(x)=1/2[f(xy)+f(x/y)] " for " x,y in R^(+) such that f(1)=0,f'(1)=2. f'(3) is equal to

Let f: R rarr R be a continuous function given by f(x+y)=f(x)+f(y) for all x,y, in R, if int_0^2 f(x)dx=alpha, then int_-2^2 f(x) dx is equal to

VK JAISWAL ENGLISH-CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION-EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. Let f (x+y) =f (x) f (y) for all x and y, and f(5)=2, f'(0)=3, then f ...

    Text Solution

    |

  2. Let f (x)= {{:(ax (x-1)+b,,, x lt 1),( x+2,,, 1 le x le 3),(px ^(2) +q...

    Text Solution

    |

  3. If y= sin (8 sin ^(-1) x ) then (1-x ^(2)) (d^(2)y)/(dx ^(2))-x (dy)/...

    Text Solution

    |

  4. If y ^(2) =4ax, then (d^(2) y)/(dx ^(2))=(ka ^(2))/( y ^(2)), where k ...

    Text Solution

    |

  5. The number of values of x , x ∈ [-2,3] where f (x) =[x ^(2)] sin (pix)...

    Text Solution

    |

  6. If f (x) is continous and differentiable in [-3,9] and f'(x) in [-2,8]...

    Text Solution

    |

  7. In f (x)= [{:(cos x ^(2),, x lt 0), ( sin x ^(3) -|x ^(3)-1|,, x ge 0)...

    Text Solution

    |

  8. Consider f(x) =x^(2)+ax+3 and g(x) =x+band F(x) = lim( n to oo) (f...

    Text Solution

    |

  9. Let f (x)= {{:(2-x"," , -3 le x le 0),( x-2"," , 0 lt x lt 4):} Then f...

    Text Solution

    |

  10. If f (x) +2 f (1-x) =x ^(2) +2 AA x in R and f (x) is a differentiable...

    Text Solution

    |

  11. Let f (x)= signum (x) and g (x) =x (x ^(2) -10x+21), then the number o...

    Text Solution

    |

  12. If (d^(2))/(d x ^(2))((sin ^(4)x+ sin ^(2)x+1)/(sin ^(2)x + si n x+1))...

    Text Solution

    |

  13. f (x) =a cos (pix)+b, f'((1)/(2))=pi and int (1//2)^(3//2) f (x) dx =2...

    Text Solution

    |

  14. Let alpha (x) = f(x) -f (2x) and beta (x) =f (x) -f (4x) and alpha '(1...

    Text Solution

    |

  15. Let f (x) =-4.e ^((1-x)/(2))+ (x ^(3))/(3 ) + (x ^(2))/(2)+ x+1 and g ...

    Text Solution

    |

  16. If y=3^(2 sin ^(-1)) then |((x ^(2) -1) y^('') +xy')/(y)| is equal to

    Text Solution

    |

  17. Let f (x)=x+ (x ^(2))/(2 )+ (x ^(3))/(3 )+ (x ^(4))/(4 ) +(x ^(5))/(5)...

    Text Solution

    |

  18. In f (x)= [{:(cos x ^(2),, x lt 0), ( sin x ^(3) -|x ^(3)-1|,, x ge 0)...

    Text Solution

    |

  19. For the curve sinx+siny=1 lying in first quadrant. If underset(xrarr0...

    Text Solution

    |

  20. Let f (x) = x tan ^(-1) (x^(2)) + x^(4) Let f ^(k) (x) denotes k ^(th)...

    Text Solution

    |

  21. If x = cos theta and y = sin^(3) theta, then |(yd ^(2)y)/(dx ^(2))+((d...

    Text Solution

    |