Results 1 to 2 of 2

Math Help - Quadratic Polynomail with chain rule

  1. #1
    Junior Member
    Joined
    Sep 2009
    Posts
    71

    Quadratic Polynomail with chain rule

    Let f(x)=sin(x)+cos(2x). Find a quadratic polynomial p(x) so that p(0)=f(0), p'(0)=f'(0) and p''(0)=f''(0).
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Nov 2008
    Posts
    461
    Hello Velvet Love

    Quote Originally Posted by Velvet Love View Post
    Let f(x)=sin(x)+cos(2x). Find a quadratic polynomial p(x) so that p(0)=f(0), p'(0)=f'(0) and p''(0)=f''(0).
    First, find the derivatives of f(x)

    It is f'(x) = cos(x)-2sin(2x) and

    f''(x) = -sin(x) -4cos(2x)

    p(x) should be quadratic, so

    p(x) = ax^2+bx+c

    In this excercise we have to find a,b,c and want to work with derivatives, so let's find p'(x) and p''(x) first

    p'(x) = 2ax+b

    p''(x) = 2a

    ( It should be p(0)=f(0), p'(0)=f'(0) and p''(0)=f''(0) )

    I suggest we start with the second derivative, because p''(x) has only one unknown in it - the 'a'. p(x) contains a,b and c.

    So

    p''(0) = f''(0)

    2a = -sin(0) -4cos(2*0)

    2a = 0 -4cos(0)

    2a = -4*1

    => a = -2.

    So p'(x) = 2ax+b = 2*(-2)a+b

    Now consider

    p'(0) = f'(0) and solve for b.

    then p(0) = f(0) and solve for c.

    Done

    Do you have some question on that?

    Yours
    Rapha
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 9
    Last Post: November 9th 2010, 02:40 AM
  2. Chain Rule Inside of Chain Rule
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 22nd 2009, 09:50 PM
  3. Replies: 5
    Last Post: October 19th 2009, 02:04 PM
  4. Replies: 3
    Last Post: May 25th 2009, 07:15 AM
  5. Replies: 2
    Last Post: December 13th 2007, 06:14 AM

Search Tags


/mathhelpforum @mathhelpforum