Home
Class 11
MATHS
A function f, defined for all positive ...

A function `f,` defined for all positive real numbers, satisfies the equation `f(x^2)=x^3` for every `x >0` . Then the value of `f^(prime)(4)` is (a)`12 `(b)` 3` (c) `3//2` (d) cannot be determined

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos
  • LINEAR INEQUALITIES

    CENGAGE ENGLISH|Exercise All Questions|68 Videos

Similar Questions

Explore conceptually related problems

A function f, defined for all positive real numbers, satisfies the equation f(x^2)=x^3 for every x >0 . Then the value of f^(prime)(4) is 12 (b) 3 (c) 3//2 (d) cannot be determined

If a differentiable function f defined for x gt0 satisfies the relation f(x^(2))=x^(3),x gt 0 , then what is the value of f'(4)?

The function f satisfies the functional equation 3f(x)+2f((x+59)/(x-1))=10 x+30 for all real x!=1. The value of f(7)i s (a) 8 (b) 4 (c) -8 (d) 11

A functions is defined for all positive numbers x as f(x) = asqrt(x) + b . What is the value of f(3) . If f(4) - f(1) = 2 and f(4) + f(1) = 10 ?

The function f satisfies the functional equation 3f(x)+2f((x+59)/(x1))=10 x+30 for all real x!=1. The value of f(7)i s 8 (b) 4 (c) -8 (d) 11

If a real valued function f(x) satisfies the equation f(x +y)=f(x)+f (y) for all x,y in R then f(x) is

The function f satisfies the functional equation 3f(x)+2f((x+59)/(x-1))=10 x+30 for all real x!=1. The value of f(7)i s 8 (b) 4 (c) -8 (d) 11

Suppose that the function F is defined for all real numbers r by the formula f(r)=2(r-1)+3 . Evaluate F at the input values 0, 2, x+2 , and f(2) .

A function f is defined by f(x^(2) ) = x^(3) AA x gt 0 then f(4) equals

A function f(x) satisfies the functional equation x^2f(x)+f(1-x)=2x-x^4 for all real x. f(x) must be

CENGAGE ENGLISH-LIMITS AND DERIVATIVES-All Questions
  1. If a x^2+2h x y+b y^2=1,t h e n(d^2y)/(dx^2) is (a)(h^2-a b)/((h x+b...

    Text Solution

    |

  2. If y=sinp x and yn is the n t h derivative of y , then |[y, y1,y2],[y3...

    Text Solution

    |

  3. A function f, defined for all positive real numbers, satisfies the eq...

    Text Solution

    |

  4. If y=x-x^2, then the derivative of y^2 with respect to x^2 is (a)1...

    Text Solution

    |

  5. The first derivative of the function [cos^(-1)(sinsqrt((1+x)/2))+x^x]...

    Text Solution

    |

  6. The function f(x)=e^x+x , being differentiable and one-to-one, has a ...

    Text Solution

    |

  7. Let h(x) be differentiable for all x and let f(x)=(k x+e^x)h(x) , w...

    Text Solution

    |

  8. Suppose y=e^(a x)+e^(b x), find y''

    Text Solution

    |

  9. If y=((a-x)sqrt(a-x)-(b-x)sqrt(x-b))/((sqrt(a-x)+sqrt(x-b)) ,then (d...

    Text Solution

    |

  10. If y= 7x^5, then (dy)/(dx)

    Text Solution

    |

  11. The nth derivative of the function f(x)=1/(1-x^2) [where in(-1,1) at ...

    Text Solution

    |

  12. Let u(x) and v(x) be differentiable functions such that (u(x))/(v(x))=...

    Text Solution

    |

  13. Statement 1: Let f: R -> R be a real-valued function AAx ,y in R such...

    Text Solution

    |

  14. Statement 1: For f(x)=sinx ,f^(prime)(pi)=f^(prime)(3pi)dot Statement...

    Text Solution

    |

  15. f:R^+ ->R is a continuous function satisfying f(x/y)=f(x)-f(y) AAx,y i...

    Text Solution

    |

  16. fn(x)=e^(f(n-1)(x)) for all n in Na n df0(x)=x ,t h e n d/(dx){fn(x)...

    Text Solution

    |

  17. Suppose f and g are functions having second derivative f'' and g' ' ev...

    Text Solution

    |

  18. If y=e^(-x)cosxa n dyn+kn y=0,w h e r eyn=(d^(n y))/(dx^n)a n dkn are ...

    Text Solution

    |

  19. If a function is represented parametrically by the equations x=(1+log(...

    Text Solution

    |

  20. Statement 1: Leg f(x)=x[x]a n d[dot] denotes the greatest integral fun...

    Text Solution

    |