Home
Class 12
MATHS
Let f(x+y) = f(x) + f(y) - 2xy - 1 for a...

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

A

-1

B

0

C

1

D

2

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS ENGLISH|Exercise Exercise (More Than One Correct Option Type Questions)|25 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS ENGLISH|Exercise Exercise (Statement I And Ii Type Questions)|11 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 7|9 Videos
  • COMPLEX NUMBERS

    ARIHANT MATHS ENGLISH|Exercise Complex Number Exercise 8|2 Videos
  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

Similar Questions

Explore conceptually related problems

Let f((x+y)/2)=(f(x)+f(y))/2 for all real x and y. If f'(0) exists and equals-1 and f(0)=1, find f(2)

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)=

If f(x-y), f(x) f(y), and f(x+y) are in A.P. for all x, y, and f(0) ne 0, then

If f(x-y), f(x) f(y), and f(x+y) are in A.P. for all x, y, and f(0) ne 0, then

Let f:R to R be given by f(x+y)=f(x)-f(y)+2xy+1"for all "x,y in R If f(x) is everywhere differentiable and f'(0)=1 , then f'(x)=

Let f(x) is a polynomial satisfying f(x).f(y) = f(x) +f(y) + f(xy) - 2 for all x, y and f(2) = 1025, then the value of lim_(x->2) f'(x) is

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(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

If f (x+y) =f (x) f(y) for all x,y and f (0) ne 0, and F (x) =(f(x))/(1+(f (x))^(2)) then:

Let f(x+y)=f(x)+f(y)+2x y-1 for all real x and y and f(x) be a differentiable function. If f^(prime)(0)=cosalpha, the prove that f(x)>0AAx in Rdot

ARIHANT MATHS ENGLISH-CONTINUITY AND DIFFERENTIABILITY-Exercise (Single Option Correct Type Questions)
  1. Find dy/dx if y= x sinx

    Text Solution

    |

  2. Let f be differentiable function satisfying f((x)/(y))=f(x) - f(y)"for...

    Text Solution

    |

  3. Let f(x+y) = f(x) + f(y) - 2xy - 1 for all x and y. If f'(0) exists an...

    Text Solution

    |

  4. A derivable function f : R^(+) rarr R satisfies the condition f(x) - f...

    Text Solution

    |

  5. If (d(f(x)))/(dx) = e^(-x) f(x) + e^(x) f(-x), then f(x) is, (given f(...

    Text Solution

    |

  6. Let f : (0, oo) rarr R be a continuous function such that f(x) = int(0...

    Text Solution

    |

  7. For let h(x)={1/q if x=p/q and 0 if x is irrational where p & q ...

    Text Solution

    |

  8. Let f(x) = (g(x))/(h(x)), where g and h are continuous functions on th...

    Text Solution

    |

  9. Find dy/dx if y=2x^7

    Text Solution

    |

  10. if f(x) =(x-e^(x)+ cos 2x)/(x^(2)),xne0 , is continuous at x=0 , t...

    Text Solution

    |

  11. Consider the function f(x) = {{:(x{x}+1",","if",0 le x lt 1),(2-{x}","...

    Text Solution

    |

  12. Let f(x) = {{:((2^(x)+2^(3-x) - 6)/(sqrt(2^(-x))-2^(1-x))",","if",x gt...

    Text Solution

    |

  13. Let [x] denote the integral part of x in R and g(x) = x- [x]. Let f(x...

    Text Solution

    |

  14. Let f be a differentiable function on the open interval(a, b). Which o...

    Text Solution

    |

  15. Number of points where the function f(x)=(x^2-1)|x^2-x-2| + sin(|x|) i...

    Text Solution

    |

  16. Consider function f: R - {-1,1}-> R. f(x)=x/[1-|x|] Then the incorrect...

    Text Solution

    |

  17. Find dy/dx if 2y-e^x=6

    Text Solution

    |

  18. The total number of points of non-differentiability of f(x) = min[|sin...

    Text Solution

    |

  19. The function f(x)=[x]^2-[x^2] is discontinuous at (where [gamma] is t...

    Text Solution

    |

  20. The function f(x) = (x^(2) - 1)|x^(2)-6x + 5|+cos|x| is not differenti...

    Text Solution

    |