Results 1 to 3 of 3

Math Help - Is this right? Finding function f(x) given tangent slope and f''(x)

  1. #1
    Member
    Joined
    May 2008
    Posts
    77

    Is this right? Finding function f(x) given tangent slope and f''(x)

    Now I think I have the correct answer, but am not 100% sure. Is it correct, and if not, where did I screw up? Cheers.

    Question
    Find a function f(x) such that the point (1, 2) is on the graph of y =f(x), the slope of the tangent line at (1, 2) is 3 and f(x)= x 1.

    My answer:
    Equation of slope of the tangent at (1, 2) is y= 3x
    f(x)= x 1
    thus:
    f(x)= x x + c

    To find c, we need to solve:
    f(x)= x x + c = 3 at x = 1
    c = 3

    Now we can find f(x):
    f(x)= x/6 x+ 3x + c
    At the tangent point (x= 1), y= f(x) has to touch the curve y = 3x:

    c = 1/6

    f(x)= x/6 x+ 3x + 1/6
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Lord of certain Rings
    Isomorphism's Avatar
    Joined
    Dec 2007
    From
    IISc, Bangalore
    Posts
    1,465
    Thanks
    6
    Quote Originally Posted by Dr Zoidburg View Post
    Now we can find f(x):
    f(x)= x/6 x+ 3x + c
    At this point use the fact that (1,2) is on the graph. That is f(1)=2 to get
    f(1)= 1/6 1+ 31 + c = 2. This gives me c = -\frac76
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    May 2008
    Posts
    77
    D'oh!
    I made f(x) equal 3 (the slope) and not 2 (the y intercept).
    Many thanks for spotting that mistake for me. Much appreciated.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 6
    Last Post: September 11th 2011, 04:53 PM
  2. Replies: 6
    Last Post: January 12th 2011, 02:38 PM
  3. Finding the slope of the tangent
    Posted in the Calculus Forum
    Replies: 5
    Last Post: March 22nd 2010, 03:18 PM
  4. Finding slope of a tangent to a function
    Posted in the Calculus Forum
    Replies: 5
    Last Post: March 18th 2010, 12:24 PM
  5. finding the slope of the tangent line
    Posted in the Calculus Forum
    Replies: 9
    Last Post: November 30th 2009, 02:17 AM

Search Tags


/mathhelpforum @mathhelpforum