Results 1 to 4 of 4

Thread: Decreasing function

  1. #1
    Member looi76's Avatar
    Joined
    Jan 2008
    Posts
    185
    Thanks
    1

    Unhappy Decreasing function

    Question:

    The diagram shows the curve y = x^3 - 3x^2 - 9x + k, where k is constant. The curve has a minimum point on the x-axis.
    (i) Find the value of k.
    (ii) Find the coordinates of the maximum point of the curve.
    (iii) State the set of values of x for which x^3 - 3x^2 - 9x + k is a decreasing function of x.

    Attempt:
    (i) k = 27
    (ii) (-1,32)
    (iii) I don't know how to get the decreasing order?!...
    Follow Math Help Forum on Facebook and Google+

  2. #2
    GAMMA Mathematics
    colby2152's Avatar
    Joined
    Nov 2007
    From
    Alexandria, VA
    Posts
    1,172
    Thanks
    1
    Awards
    1
    Keep in mind that the function is decreasing before it hits that minimum.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member looi76's Avatar
    Joined
    Jan 2008
    Posts
    185
    Thanks
    1
    Quote Originally Posted by colby2152 View Post
    Keep in mind that the function is decreasing before it hits that minimum.
    Thanks colby2152, but I don't know which formula to use!..
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Lord of certain Rings
    Isomorphism's Avatar
    Joined
    Dec 2007
    From
    IISc, Bangalore
    Posts
    1,465
    Thanks
    6
    Quote Originally Posted by looi76 View Post
    Question:

    The diagram shows the curve y = x^3 - 3x^2 - 9x + k, where k is constant. The curve has a minimum point on the x-axis.
    (i) Find the value of k.
    (ii) Find the coordinates of the maximum point of the curve.
    (iii) State the set of values of x for which x^3 - 3x^2 - 9x + k is a decreasing function of x.

    Attempt:
    (i) k = 27
    (ii) (-1,32)
    (iii) I don't know how to get the decreasing order?!...
    Well actually its quite clear from the graph that it is decreasing between the maximum and the minimum. So for -1 < x < 3, we have the function decreasing....

    A calculus way of showing it is computing the derivative of f(x) and if the derivative is less than 0 then the function is decreasing.

    So f'(x) = 3x^2 - 6x -9 < 0 \Rightarrow 3(x^2 - 2x - 3) = 3(x-3)(x+1) < 0 \Rightarrow x \in (-1,3)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. decreasing function
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: Apr 27th 2011, 06:19 AM
  2. non-decreasing function in n-variables
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: Dec 8th 2010, 04:29 AM
  3. Decreasing function
    Posted in the Calculus Forum
    Replies: 4
    Last Post: Oct 29th 2008, 05:26 PM
  4. decreasing function
    Posted in the Math Software Forum
    Replies: 0
    Last Post: Mar 19th 2008, 02:59 AM
  5. decreasing function
    Posted in the Calculus Forum
    Replies: 6
    Last Post: Aug 1st 2007, 01:25 PM

Search Tags


/mathhelpforum @mathhelpforum