Home
Class 12
MATHS
g(x+y)=g(x)+g(y)+3xy(x+y)AA x, y in R" a...

`g(x+y)=g(x)+g(y)+3xy(x+y)AA x, y in R" and "g'(0)=-4.`
The value of g'(1) is

A

0

B

1

C

-1

D

none of these

Text Solution

AI Generated Solution

To solve the problem, we will follow these steps: ### Step 1: Differentiate the given functional equation We start with the equation: \[ g(x+y) = g(x) + g(y) + 3xy(x+y) \] We will differentiate both sides with respect to \( x \) while treating \( y \) as a constant. ...
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Matrix Match Type|6 Videos

  • DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Numerical Value Type|45 Videos

  • DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Multiple Correct Answers Type|29 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE ENGLISH|Exercise Matrix Match Type|5 Videos

  • DOT PRODUCT

    CENGAGE ENGLISH|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

g(x+y)=g(x)+g(y)+3xy(x+y)AA x, y in R" and "g'(0)=-4. Number of real roots of the equation g(x) = 0 is

g(x+y)=g(x)+g(y)+3xy(x+y)AA x, y in R" and "g'(0)=-4. For which of the following values of x is sqrt(g(x)) not defined ?

Let g(x+(1)/(y)) + g(x-(1)/(y)) = 2g(x) g((1)/(y)) AA x, y in R, y !=0 and g(0) = 0. Then find g(1), g(2) .

Let f :R to R be a continous and differentiable function such that f (x+y ) =f (x). F(y)AA x, y, f(x) ne 0 and f (0 )=1 and f '(0) =2. Let g (xy) =g (x). g (y) AA x, y and g'(1)=2.g (1) ne =0 The number of values of x, where f (x) g(x):

Let g(x) be a polynomial function satisfying g(x).g(y) = g(x) + g(y) + g(xy) -2 for all x, y in R and g(1) != 1 . If g(3) = 10 then g(5) equals

Find the area of the region bounded by the curves y=f(x), y=|g(x)| and lines x = 0, x = 2 , where f and g are continuous functions satisfying f(x+y)=f(x)+f(y)-8xy for all x,y in R and g(x+y)=g(x)+g(y)+3xy(x+y) for all x,y in R . Also f\'(0) = 8 and g\'(0)=-4 .

Let a real valued function f satisfy f(x + y) = f(x)f(y)AA x, y in R and f(0)!=0 Then g(x)=f(x)/(1+[f(x)]^2) is

Let y = f (x) such that xy = x+y +1, x in R-{1} and g (x) =x f (x) The minimum value of g (x) is:

Let f :R to R be a continous and differentiable function such that f (x+y ) =f (x). F(y)AA x, y, f(x) ne 0 and f (0 )=1 and f '(0) =2. Let g (xy) =g (x). g (y) AA x, y and g'(1)=2.g (1) ne =0 Identify the correct option:

Let g: RvecR be a differentiable function satisfying g(x)=g(y)g(x-y)AAx , y in R and g^(prime)(0)=aa n dg^(prime)(3)=bdot Then find the value of g^(prime)(-3)dot

CENGAGE ENGLISH-DIFFERENTIATION-Linked Comprehension Type
  1. f:RrarrR,f(x)=x^(3)+x^(2)f'(1)+xf''(2)+f'''(3)" for all "x in R. f(x...

    Text Solution

    |

  2. f:RrarrR,f(x)=x^(3)+x^(2)f'(1)+xf''(2)+f'''(3)" for all "x in R. The...

    Text Solution

    |

  3. Repeated roots : If equation f(x) = 0, where f(x) is a polyno- mial fu...

    Text Solution

    |

  4. Repeated roots : If equation f(x) = 0, where f(x) is a polyno- mial fu...

    Text Solution

    |

  5. Repeated roots : If equation f(x) = 0, where f(x) is a polyno- mial fu...

    Text Solution

    |

  6. Equation x^(n)-1=0, ngt1, n in N," has roots "1,a(1),a(2),…,a(n-1). ...

    Text Solution

    |

  7. Equation x^(n)-1=0,ngt1,ninN, has roots 1,a(1),a(2),...,a(n),. The val...

    Text Solution

    |

  8. Equation x^(n)-1=0, ngt1, n in N," has roots "1,a(1),a(2),…,a(n-1). ...

    Text Solution

    |

  9. f(x)=x^(2)+xg'(1)+g''(2)and g(x)=f(1)x^(2)+xf'(x)+f'(x). The value o...

    Text Solution

    |

  10. f(x)=x^(2)+xg'(1)+g''(2)and g(x)=f(1)x^(2)+xf'(x)+f'(x). The value o...

    Text Solution

    |

  11. f(x)=x^(2)+xg'(1)+g''(2)and g(x)=f(1)x^(2)+xf'(x)+f'(x). The domain ...

    Text Solution

    |

  12. g(x+y)=g(x)+g(y)+3xy(x+y)AA x, y in R" and "g'(0)=-4. Number of real...

    Text Solution

    |

  13. g(x+y)=g(x)+g(y)+3xy(x+y)AA x, y in R" and "g'(0)=-4. For which of t...

    Text Solution

    |

  14. g(x+y)=g(x)+g(y)+3xy(x+y)AA x, y in R" and "g'(0)=-4. The value of g...

    Text Solution

    |

  15. A curve is represented parametrically by the equations x=f(t)=a^(In(b^...

    Text Solution

    |

  16. A curve is represented parametrically by the equations x=f(t)=a^(In(b^...

    Text Solution

    |

  17. A curve is represented parametrically by the equations x=f(t)=a^(In(b'...

    Text Solution

    |

  18. Let f: R rarr R be a differentiable function satisfying f(x+y)=f(x)+f(...

    Text Solution

    |

  19. Let f: R rarr R be a differentiable function satisfying f(x+y)=f(x)+f(...

    Text Solution

    |

  20. If roots of an equation x^n-1=0a r e1,a1,2, a(n-1), then the value of...

    Text Solution

    |