Page 1 of 3 123 LastLast
Results 1 to 15 of 41
Like Tree6Thanks

Math Help - sketching curve graph

  1. #1
    Member
    Joined
    Mar 2012
    From
    nyc
    Posts
    120
    Thanks
    1

    sketching curve graph

    hello everyone....im really hoping someone can help me, im in somewhat of a fix.

    the problem is: x3+2x2-x-2

    i have to:

    find where f(x) is increasing/decreasing
    where it is concave up/concave down
    local max/min
    and then finally sketch the curve of the graph

    my first step is to take the derivative, which is : f'(x)=3x2+4x-1
    im a bit lost as to what i should do after this. i know i have to find the critical points where x=0 and is undefined.
    when the whole equation =0, x= -4/3? the derivative cant be further factored, right?

    i cant get past this point, so any guidance is highly appreciated. thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,406
    Thanks
    1294

    Re: sketching curve graph

    f(x) is increasing where f'(x) > 0.
    f(x) is decreasing where f'(x) < 0.
    Local maxima and minima occur where f'(x) = 0. If it's a maximum then f''(x) < 0 at that point, and if it's a minimum then f''(x) > 0 at that point.

    To sketch the graph, find the critical points, the x and y intercepts and then you have enough info to sketch...
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Mar 2012
    From
    nyc
    Posts
    120
    Thanks
    1

    Re: sketching curve graph

    yes i know that, but im stuck after getting the first derivative. i know i have to get the critical points after that but, how do i make that derivative equal 0 and get a value for it? it dosnt factor...
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Mar 2010
    Posts
    980
    Thanks
    236

    Re: sketching curve graph

    To find out where 3x^2+4x-1 is zero, since it won't factor easily, use the quadratic equation....

    - Hollywood
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,406
    Thanks
    1294

    Re: sketching curve graph

    Quote Originally Posted by hollywood View Post
    To find out where 3x^2+4x-1 is zero, since it won't factor easily, use the quadratic equation....

    - Hollywood
    Use the Quadratic FORMULA
    Thanks from hollywood
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Mar 2012
    From
    nyc
    Posts
    120
    Thanks
    1

    Re: sketching curve graph

    using the quadratic formula (just the cas calc) i got x=2 or x=-1 or x=1

    does that sound about right?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Mar 2012
    From
    nyc
    Posts
    120
    Thanks
    1

    Re: sketching curve graph

    ok im doing something wrong because im just not getting it. can someone PLEASE just start me off?? get me past this particular step..thanks
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: sketching curve graph

    You have the correct first derivative...and you should know that a quadratic has only two roots, I don't know how you obtained three. Don't use the CAS, plug into the quadratic formula, and what do you find...show your work so we can see what you did wrong if you don't get the correct roots.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Member
    Joined
    Mar 2012
    From
    nyc
    Posts
    120
    Thanks
    1

    Re: sketching curve graph

    https://www.dropbox.com/s/7vw527ndhy...2000.22.56.jpg

    how's this??? why does this looks so complicated??

    where do i go from here. find at which inteervals the function is increasing/decreasing?? how do u do that with square roots? (hate them, btw)
    Last edited by noork85; May 3rd 2013 at 08:35 PM.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: sketching curve graph

    You are correct...we don't always get rational roots. Now these two roots give you 3 open intervals on the real number line, and since the roots are not repeated, we know the sign of the derivative will alternate across the intervals, so I would choose the test point of zero in the middle interval. What is the sign of f'(0)? Once you have this, then you know the sign of the derivative is the opposite of this on the other two intervals. And this will tell you where the original function is increasing/decreasing. What do you find?
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Member
    Joined
    Mar 2012
    From
    nyc
    Posts
    120
    Thanks
    1

    Re: sketching curve graph

    im lost......but is this close to what im supposed to do??

    https://www.dropbox.com/s/ns1bp0mkom...2000.53.26.jpg
    Follow Math Help Forum on Facebook and Google+

  12. #12
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: sketching curve graph

    You have correctly used the roots of the derivative to divide the number line, but the sign associated with the leftmost interval should be positive, for the reason I cited above. If you wish to test all 3 intervals, I would use integers...-2 for the leftmost interval, 0 for the middle and 1 for the rightmost. Get decimal approximations for the roots of the derivative, and you will see why these work.
    Follow Math Help Forum on Facebook and Google+

  13. #13
    Member
    Joined
    Mar 2012
    From
    nyc
    Posts
    120
    Thanks
    1

    Re: sketching curve graph

    is that always the case? since f(0) is (-), then the other two intervals will always be positive?

    and just to be sure, to get the signs, im plugging in numbers into the derivative or the original equation? i plugged (-1) and (1) on the left and right intervals into the derivative. but i think youre supposed to use the original, no ?
    Follow Math Help Forum on Facebook and Google+

  14. #14
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: sketching curve graph

    It is only the case when the roots are of odd multiplicity, here your two roots are both of multiplicity 1, so we know the sign will alternate.

    You want to check the sign of the derivative, since a positive derivative means the original function is increasing, while a negative derivative means it is decreasing. -1 is in the same interval as 0, that's why I suggest using -2 as a test point for the leftmost interval.
    Follow Math Help Forum on Facebook and Google+

  15. #15
    Member
    Joined
    Mar 2012
    From
    nyc
    Posts
    120
    Thanks
    1

    Re: sketching curve graph

    okay...gotcha.

    now the next step is finding the inflection point, right? how does this look?

    is it an inflection point? function is increasing on both sides.

    https://www.dropbox.com/s/h7hviziib6...2001.24.56.jpg
    Last edited by noork85; May 3rd 2013 at 09:28 PM.
    Follow Math Help Forum on Facebook and Google+

Page 1 of 3 123 LastLast

Similar Math Help Forum Discussions

  1. curve sketching!! help!
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 27th 2013, 07:08 PM
  2. Curve Sketching
    Posted in the Calculus Forum
    Replies: 2
    Last Post: August 22nd 2009, 11:33 AM
  3. Curve Sketching
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 20th 2009, 05:37 PM
  4. Curve Sketching
    Posted in the Calculus Forum
    Replies: 4
    Last Post: April 27th 2009, 02:24 AM
  5. Curve Sketching
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 6th 2008, 06:18 AM

Search Tags


/mathhelpforum @mathhelpforum