Results 1 to 2 of 2

Math Help - Local Extrema Question Again, With Two Parts

  1. #1
    Junior Member
    Joined
    Sep 2009
    Posts
    62

    Local Extrema Question Again, With Two Parts

    I recently asked a question similar to this, but that question only wanted a local maximum. Now I have one asking for values to get a certain max AND min.

    Problem: Find values of a, b, and c so that the function f(x) = 2x^3 + ax^2 + bx + c has a local maximum at the point (-2, 22) and a local minimum at the point ( 1, -5).





    So far, I've taken the derivative, which is 6x^2 + 2ax + b, then I solved for b, which is b = -x(6x + 2a). I then set b to 0 and solved for x, getting x = 0 and x = \frac{-2a}{6}.

    Then, plugging in -2 for x, I got a = 6.

    I don't think what I'm doing is right. How do I solve this taking into account both a max AND a min?
    Could you please show your steps and explain a little about what you do and why? Thank you SO much! I'm really struggling with these problems.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Oct 2009
    From
    Brisbane
    Posts
    311
    Thanks
    2
    The derivative which you have found correctly will be equal to 0 when x=-2 and x=1 (the turning points). So put -2 in for x to get an equation involving a and b.
    Then do the same for x=1 to get another equation involving a and b. Solve simultaneously to find a and b.
    Then put these values into f(x) so that all you still need is to find c.
    Then use the fact that f(-2)=22 to find c. Check it with the other point (1, -5).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Question on local extrema problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: June 29th 2010, 05:53 PM
  2. Absolute Extrema, Local Extrema
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 23rd 2009, 04:08 AM
  3. Replies: 1
    Last Post: November 19th 2009, 12:22 AM
  4. Local Extrema Question
    Posted in the Calculus Forum
    Replies: 4
    Last Post: October 26th 2009, 11:03 PM
  5. local extrema
    Posted in the Calculus Forum
    Replies: 1
    Last Post: June 3rd 2009, 10:50 PM

Search Tags


/mathhelpforum @mathhelpforum