Results 1 to 2 of 2

Math Help - Cubic polynomials

  1. #1
    Member
    Joined
    Sep 2009
    Posts
    80

    Cubic polynomials

    Eh. Here's the problem:

    "A cubic polynomial is given by f(x)=ax^3+bx^2+30x+k where a, b, and k are constants. The function f(x) has a local minimum at (-1,-10) and a point of inflection at x=2.

    a) Find the values of a, b, and k.

    b) Use the second derivative to verify that (-1,-10) really is a local minimum for your function.

    c) Find the location of any local maximums for your function. Verify that they are indeed a local maximum."

    Here's what I've done so far..

    I've found the first derivative, f(x)= 3ax^2 + 2bx + 30
    and the second derivative, f(x)= 6ax + 2b.

    I then plugged the value of x=1 into the first derivative, getting 3a-2b+30.
    I also plugged the inflection point of x=2 into the second derivative and got
    12a+2b.

    From there, I can't seem to remember what to do. Help, please? D:
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member Shanks's Avatar
    Joined
    Nov 2009
    From
    BeiJing
    Posts
    374
    solve the following linear equations :
    f(-1)=a(-1)^3+b(-1)^2+30(-1)+k=-10
    f'(-1)= 3a(-1)^2 + 2b(-1) + 30=0
    f''(2)= 12a + 2b=0
    to get the value of a, b, and k.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Solving cubic polynomials
    Posted in the Algebra Forum
    Replies: 9
    Last Post: October 26th 2009, 11:55 PM
  2. General Question about Cubic Polynomials
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: October 11th 2009, 05:54 AM
  3. Factoring cubic and further polynomials
    Posted in the Algebra Forum
    Replies: 5
    Last Post: August 31st 2009, 02:16 PM
  4. Cubic polynomials- finding unknowns
    Posted in the Algebra Forum
    Replies: 3
    Last Post: June 15th 2009, 03:55 AM
  5. cubic polynomials
    Posted in the Algebra Forum
    Replies: 2
    Last Post: May 3rd 2008, 06:01 PM

Search Tags


/mathhelpforum @mathhelpforum