Results 1 to 2 of 2

Math Help - Equation for tangent line of inverse function.

  1. #1
    Newbie
    Joined
    Sep 2011
    Posts
    11

    Equation for tangent line of inverse function.

    Let f(x)=(x^4)+(x^3)+1
    Let g(x) be the inverse of f(x) and define F(x)=f(2g(x)). Find an equation for the tangent line to y=F(x) at x=3.


    The answer the book gives is y=(88x-89)/7 I just have no clue how to get there! Please help!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,393
    Thanks
    1327

    Re: Equation for tangent line of inverse function.

    If y= f(2f^{-1}(x)), by the chain rule, the derivative is y'= f'(2f^{-1}(x))(2(f^{-1}(x)'. Further, ( (f^{-1})'= \frac{1}{f'(y)} where y is such that f(y)= x. Here, f(x)= x^4+ x^3+ 1 so f'(x)= 4x^3+ 3x^2. g(x) will be the value, y, such that f(y)= y^4+ y^3+ 1= 3. Fortunately, it is clear that y= 1 satisfies that equation so g(3)= f^{-1}(3)= 1
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 6
    Last Post: January 12th 2011, 02:38 PM
  2. Replies: 7
    Last Post: December 5th 2009, 08:53 AM
  3. Replies: 5
    Last Post: February 23rd 2009, 03:49 PM
  4. Replies: 1
    Last Post: October 25th 2008, 01:13 PM
  5. tangent line to inverse function at P
    Posted in the Calculus Forum
    Replies: 2
    Last Post: August 21st 2008, 01:40 PM

Search Tags


/mathhelpforum @mathhelpforum