Home
Class 12
MATHS
In a question a student was given to fin...

In a question a student was given to find the derivative of the product of two functions `fa n dgdot` The student by mistake thought `(fg)^'=f'g'` for his question `f(x)=x^3` and he got the correct answer. Given that `g(4)=1.` Then which of the following is false? `g(5)=1/8` b. `f^(prime)(x)<0` c.`f(0)<0` d. none of these

Promotional Banner

Topper's Solved these Questions

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|102 Videos
  • COORDINATE SYSTEM

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|2 Videos

Similar Questions

Explore conceptually related problems

If RR is the set of real numbers and f(x)=|x|,g(x)=x , find the product function fg.

Two real function f and g are defined respectively by f(x) = sqrt(x-3) and g(x)=sqrt(x^2-9). Find each of the following functions : fg

If g is the inverse of a function f and f(x)=1/(1+x^5) , Then g'(x) i equal to :

Two real valued functions f and g are defined respectively by f(x)=log_e(1-x) and g(x)=[x], find the following functions : fg

If the function f(x)=x^(3)+e^((x)/(2)) and g(x)=f^(-1)(x) , then the value of g'(1) is

Two real function f and g are defined respectively by f(x) = sqrt(x-3) and g(x)=sqrt(x^2-9). Find each of the following functions : f+g

Two real function f and g are defined respectively by f(x) = sqrt(x-3) and g(x)=sqrt(x^2-9). Find each of the following functions : f-g

Two real function f and g are defined respectively by f(x) = sqrt(x-3) and g(x)=sqrt(x^2-9). Find each of the following functions : (f)/(g)

If f(x)=e^x and g(x) =log_(e)x, then find (f+g)(1) and fg(1).

Two real valued functions f and g are defined respectively by f(x)=log_e(1-x) and g(x)=[x], find the following functions : f+g

CENGAGE PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. Suppose f: R->R^+ be a differentiable function such that 3f(x+y)=f(x)f...

    Text Solution

    |

  2. Vertices of a variable acute angled triangle A B C lies on a fixed cir...

    Text Solution

    |

  3. In a question a student was given to find the derivative of the prod...

    Text Solution

    |

  4. A nonzero polynomial with real coefficient has the property that f(x)=...

    Text Solution

    |

  5. If 'f' is an increasing function from RtoR such that f^(prime)prime(x)...

    Text Solution

    |

  6. If x=(1+t)/(t^(3)),y=(3)/(2t^(2))+(2)/(t) then x((dy)/(dx))^(3)-(dy)/(...

    Text Solution

    |

  7. Let f(x)={2/(1+x^2),xi sr a t ion a l b ,xi sr a t ion a l has exactly...

    Text Solution

    |

  8. If f(x)={sin((a-x)/2)t a n[(pix)/(2a)] for x > a and ([cos((pix)/(2a...

    Text Solution

    |

  9. Let f(x)={((alpha cotx)/x+beta/x^2 ,, 0<|x|lt=1),(1/3 ,, x=0):}. If f...

    Text Solution

    |

  10. Statement 1: Minimum number of points of discontinuity of the functi...

    Text Solution

    |

  11. Let f(x)=[tanx[cotx]], x in [(pi)/(12),(pi)/(2)), (where [.] denotes t...

    Text Solution

    |

  12. Let f[-2,2]rarrR be a continuous function such that f(x)assumes only i...

    Text Solution

    |

  13. If f(x)=prod(n=1)^(100)(x-n)^(n(101-n)); then (f(101))/(f'(101))=

    Text Solution

    |

  14. A curve in the xy-plane is parametrically given by x=t+t^3a n dy=t^2,w...

    Text Solution

    |

  15. Number of points of discontinuity of f(x)=[sin^(-1)x]-[x] in its domai...

    Text Solution

    |

  16. If g(x)=(lim)(mtooo)(x^mf(x)+h(x)+3)/(2x^m+4x+1) when x!=1a n dg(1)=e^...

    Text Solution

    |

  17. Suppose |[f'(x),f(x)],[f''(x),f'(x)]|=0 is continuously differentiable...

    Text Solution

    |

  18. If f(x)=|[(x-a)^4, (x-a)^3, 1] , [(x-b)^4, (x-b)^3,1] , [(x-c)^4, (x-c...

    Text Solution

    |

  19. Let (f(x+y)-f(x))/2=(f(y)-a)/2+x y for all real xa n dydot If f(x) is ...

    Text Solution

    |

  20. A function f: R -> R satisfies the equation f(x)f(y)-f(x y)=x+yAAx ,y ...

    Text Solution

    |