Results 1 to 4 of 4

Math Help - local max/min and inflection point

  1. #1
    Junior Member
    Joined
    Sep 2008
    Posts
    30

    Exclamation local max/min and inflection point

    The derivative of a function is f'(x)= (x-1)˛(x+3).
    Find the value of x at each point where f has a
    (a) local maximum
    (b) local minimum
    (c) point of inflection

    I got that the maximum is at x=-3, and minimum at x=1. I got x=-5/3 and x=1 as points of inflection.
    Can anyone tell me if I'm right, please?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Dec 2008
    Posts
    130
    Quote Originally Posted by h4hv4hd4si4n View Post
    The derivative of a function is f'(x)= (x-1)˛(x+3).
    Find the value of x at each point where f has a
    (a) local maximum
    (b) local minimum
    (c) point of inflection

    I got that the maximum is at x=-3, and minimum at x=1. I got x=-5/3 and x=1 as points of inflection.
    Can anyone tell me if I'm right, please?
    solve where derivative is zero and then check the signs on different intervals
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member mollymcf2009's Avatar
    Joined
    Jan 2009
    From
    Charleston, SC
    Posts
    490
    Awards
    1
    The answers you have are for the graph of f'. You use f' to find where f is increasing and decreasing. If you put the graph of f' into your graphing calculator, you will see that it is negative (below the x axis) from - infinity to -3 and positive (above the x axis) from -3 to infinity. What this tells you is that the graph of f is decreasing (could be negative or positive) to the left of -3 and increasing (negative or positive) from -3 to 1 and also to the right of 1.

    A minimum or maximum on the graph of f only occurs if there is a change from decreasing to increasing or vice versa. Since you only have one change of sign (which occurs when the derivative =0) this will be your local minimum. The graph of f does not have a local maximum. Now, f' does = 0 at x=1, but notice in the equation of f' that this zero has a power of 2. This tells you that it does equal zero at 1, but it only touches the x-axis, it does not cross it. So, there is no sign change at x=1 and therefore is not a candidate for max or min.

    Your inflection points are correct!!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by GaloisTheory1 View Post
    solve where derivative is zero and then check the signs on different intervals
    The OP has probably done this and is seeking confirmation of his/her answers.

    @OP: Your answers are correct. Note that there is actually a stationary point of inflection at x = 1.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: July 25th 2011, 05:31 AM
  2. local man, local min, inflection point problem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 28th 2011, 12:44 AM
  3. Replies: 1
    Last Post: April 20th 2010, 08:33 PM
  4. Local minimum and inflection
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 7th 2010, 10:00 PM
  5. Replies: 4
    Last Post: January 16th 2009, 08:46 AM

Search Tags


/mathhelpforum @mathhelpforum