Home
Class 12
MATHS
Let f(x) be continuous and differentiabl...

Let f(x) be continuous and differentiable function for all reals and f(x + y) = f(x) - 3xy + f(y). If `lim_(h to 0)(f(h))/(h) = 7`, then the value of f'(x) is

A

`-3x`

B

7

C

`-3x + 7`

D

`2f(x) + 7`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|26 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|11 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise For Session 7|10 Videos

  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|43 Videos

  • COORDINATE SYSTEM AND COORDINATES

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

Similar Questions

Explore conceptually related problems

Let f(x) be continuous and differentiable function for all real x and f(x+y)=f(x)-xy+f(y) if lim_(h rarr0)(f(h))/(h)=2 then f(5)-f(3) is

Let f(x) be continuous and differentiable function everywhere satisfying f(x+y)=f(x)+2y^(2)+kxy and f(1)=2, f(2)=8 then the value of f(3) equals

Suppose that fis differentiable function with the proporty f(x+y)=f(x)+f(y)+x^(2)y and lim_(x rarr0)(f(x))/(x)=0 ,then find the value of f'(10)

If f(x) be a differentiable function for all positive numbers such that f(x.y)=f(x)+f(y) and f(e)=1 then lim_(x rarr0)(f(x+1))/(2x)

Let f: R rarr R be a differentiable function satisfying f(x+y)=f(x)+f(y)+x^(2)y+xy^(2) for all real numbers x and y. If lim_(xrarr0) (f(x))/(x)=1, then The value of f'(3) is

Let f: R rarr R be a differentiable function satisfying f(x+y)=f(x)+f(y)+x^(2)y+xy^(2) for all real numbers x and y. If lim_(xrarr0) (f(x))/(x)=1, then The value of f(9) is

If f(x) is a differentiable function of x then lim_(h rarr0)(f(x+3h)-f(x-2h))/(h)=

Let f be a differentiable function such that f(1) = 2 and f'(x) = f (x) for all x in R . If h(x)=f(f(x)), then h'(1) is equal to

ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (Single Option Correct Type Questions)
  1. Consider function f: R - {-1,1}-> R. f(x)=x/[1-|x|] Then the incorrect...

    Text Solution

    |

  2. If the functions f : R -> R and g : R -> R are such that f(x) is conti...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  6. If f(x) = {{:((1)/(e^(1//x))",",x ne 0),(0",",x = 0):} then

    Text Solution

    |

  7. Given f(x) = (e^(x)-cos 2x - x)/(x^(2)),"for x" in R-{0} g(x) = {{:(f(...

    Text Solution

    |

  8. The function g(x) = {{:(x+b",",x lt 0),(cos x",",x ge 0):} cannot be m...

    Text Solution

    |

  9. The graph of function f contains the point P(1, 2) and Q(s, r). The e...

    Text Solution

    |

  10. Consider f(x)=[(2(sinx-sinx-sin^3x))+|sinx-sin^3 x|)/(2(sinx-sin^3 x)...

    Text Solution

    |

  11. If f(x+y) = f(x) + f(y) + |x|y+xy^(2),AA x, y in R and f'(0) = 0, then

    Text Solution

    |

  12. Let f(x) = max. {|x^2 - 2 |x||,|x|} and g(x) = min. {|x^2 - 2|x||, |x|...

    Text Solution

    |

  13. Let g(x)=[(3x^2-4sqrtx+1, x<1),(ax+b, x>=1)) If g(x) is continuous and...

    Text Solution

    |

  14. Let f(x) be continuous and differentiable function for all reals and f...

    Text Solution

    |

  15. Let [x] be the greatest integer function f(x)=(sin(1/4(pi[x]))/([x])) ...

    Text Solution

    |

  16. If f(x) = {{:(b([x]^(2)+[x])+1",","for",x ge -1),(sin(pi(x+a))",","for...

    Text Solution

    |

  17. If both f(x) & g(x) are differentiable functions at x=x0then the fun...

    Text Solution

    |

  18. Number of points of non-differentiability of the function g(x) = [x^2...

    Text Solution

    |

  19. If f(x) = ({x}g(x))/({x}g(x)) is a periodic function with period (1)/(...

    Text Solution

    |

  20. If f((x)/(y))=(f(x))/(f(y)) for all x, y in R, y ne 0 and f'(x) exists...

    Text Solution

    |