Home
Class 12
MATHS
Let F(x)=f(x) g(x) h(x) for all real x, ...

Let `F(x)=f(x) g(x) h(x)` for all real x, where f(x), g(x), and h(x) are differentiable functions. At some point `x_(0),F'(x_(0))=21F(x_(0)),f'(x_(0))=4f(x_(0)),g'(x_(0))=-7g(x_(0)), and h'(x_(0))=kh(x_(0)).` Then k = -

A

12

B

12

C

24

D

-24

Text Solution

Verified by Experts

The correct Answer is:
C
We have,
`F(x)=f(x)g(x)h(x)`
`implies" "logF(x)=logf(x)+logg(x)+logh(x)`
Differentiating both sides w.r.t. x, we get
`(F'(x))/(F(x))=(f'(x))/(f(x))+(g'(x))/(g(x))+(h'(x))/(h(x))`
`implies" "(F'(x_(0)))/(F(x_(0)))=(f'(x_(0)))/(f(x_(0)))+(g'(x_(0)))/(g(x_(0)))+(h'(x_(0)))/(h(x_(0)))`
`implies" "21=4-7+lambda`
`implies" "lambda=24`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|58 Videos

  • DIFFERENTIATION

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

  • DIFFERENTIATION

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

  • DIFFERENTIALS, ERRORS AND APPROXIMATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|17 Videos

  • ELLIPSE

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|29 Videos

Similar Questions

Explore conceptually related problems

Let F(x)=f(x)g(x)h(x) for all real x ,w h e r ef(x),g(x),a n dh(x) are differentiable functions. At some point x_0,F^(prime)(x_0)=21 F(x_0),f^(prime)(x_0)=4f(x_0),g^(prime)(x_0)=-7g(x_0), and h^(prime)(x_0)=kh(x_0) . Then k is________

Let F(x)=f(x)g(x)h(x) for all real x ,w h e r ef(x),g(x),a n dh(x) are differentiable functions. At some point x_0,F^(prime)(x_0)=21 F(x_0),f^(prime)(x_0)=4f(x_0),g^(prime)(x_0)=-7g(x_0), and h^(prime)(x_0)=kh(x_0), then the value of k is

Let F(x)=f(x)g(x)h(x) for all real x ,w h e r ef(x),g(x),a n dh(x) are differentiable functions. At some point x_0,F^(prime)(x_0)=21 F(x_0),f^(prime)(x_0)4f(x_0),g^(prime)(x_0)=-7g(x_0), then the value of g^(prime)(1) is ________

f(x) and g(x) are two differentiable functions in [0,2] such that f"(x)=g"(x)=0, f'(1)=2, g'(1)=4, f(2)=3, g(2)=9 then f(x)-g(x) at x=3/2 is

If both f(x) & g(x) are differentiable functions at x=x_0 then the function defiend as h(x) =Maximum {f(x), g(x)}

Let f(x) and g(x) be defined and differntiable for all x ge x_0 and f(x_0)=g(x_0) f(x) ge (x) for x gt x_0 then

Let g(x)=f(x)+f(1-x) and f''(x)<0 , when x in (0,1) . Then f(x) is

If f(x) is a differentiable function satisfying |f'(x)|le4AA x in [0, 4] and f(0)=0 , then

If f(x)=e^(x)g(x),g(0)=2,g'(0)=1, then f'(0) is

Let f be a twice differentiable function such that f''(x)=-f(x)" and "f'(x)=g(x)."If "h'(x)=[f(x)]^(2)+[g(x)]^(2), h(1)=8" and "h(0)=2," then "h(2)=

OBJECTIVE RD SHARMA ENGLISH-DIFFERENTIATION-Section I - Solved Mcqs
  1. Let f be a differentiable function satisfying [f(x)]^(n)=f(nx) for all...

    Text Solution

    |

  2. If f (x) =|x-1|and g (x) =f (f (f (x))), then g' (x) is equal to:

    Text Solution

    |

  3. Let F(x)=f(x) g(x) h(x) for all real x, where f(x), g(x), and h(x) are...

    Text Solution

    |

  4. If g is the inverse function of and f'(x) = sin x then prove that g'(x...

    Text Solution

    |

  5. Let f(x) be a second degree polynomial function such that f(-1)=f(1) a...

    Text Solution

    |

  6. Find the derivative of f(tan x) w.r.t. g (sec x) at x=(pi)/(4), where ...

    Text Solution

    |

  7. Find the derivative of sec^(-1)((1)/(2x^(2)-1))" w.r.t. "sqrt(1-x^(2))...

    Text Solution

    |

  8. The derivative of sin^(-1)(3x-4x^(3)) with respect to sin^(-1)x, is

    Text Solution

    |

  9. If f(x)=cos{(pi)/(2)[x]-x^(3)},1ltxlt2, and [x] denotes the greatest i...

    Text Solution

    |

  10. Let f(x)=sinx,g(x)=2x" and "h(x)=cosx. If phi(x)=["go"(fh)](x)," then ...

    Text Solution

    |

  11. Let f(x) be a polynomial function satisfying f(x)+f((1)/(x))=f(x)f((1...

    Text Solution

    |

  12. If f(x)=|{:(x^(n),sinx,cosx),(n!,"sin"(npi)/(2),"cos"(npi)/(2)),(a,a^(...

    Text Solution

    |

  13. If y=f((2x-1)/(x^2+1))andf^'(x)=sinx^2, then find (dy)/(dx)

    Text Solution

    |

  14. Let f be a differentiable function defined for all x in R such that f(...

    Text Solution

    |

  15. If f(x) = cos x cos 2x cos 4x cos 8x cos 16x then find f' (pi/4)

    Text Solution

    |

  16. If f(x) = cos x\ cos 2x\ cos 2^2\ x\ cos 2^3 x\ ....cos2^(n-1) x and n...

    Text Solution

    |

  17. f^(prime)(x)=varphi^(prime)(x)=f(x) for all xdot Also, f(3)=5a n df^(p...

    Text Solution

    |

  18. If f'(x)= sqrt(2x^(2)-1) and y=f(x^(2)),then (dy)/(dx) at x = 1 is

    Text Solution

    |

  19. Let f be a one-one function satisfying f'(x)=f(x) then (f^-1)''(x) is ...

    Text Solution

    |

  20. Differentiate sec^-1""(1)/(2x^2-1) with respect to sqrt(1-x^2)

    Text Solution

    |