IGCSE/GCSE/O & A Level/IB/University Student Forum

Qualification => Subject Doubts => GCE AS & A2 Level => Math => Topic started by: cashem'up on September 08, 2009, 02:18:29 pm

Title: Increasing and Decreasing funcitons....plzz help
Post by: cashem'up on September 08, 2009, 02:18:29 pm
hey guys can u plzz help me wid this....astarmathsandphysics..neone else...my teacher seemed not to teach me very well
can someone solve these:
find increasing interval of F(x):=
1.  2x3-9x2-24x+7
2.  x4-2x2
3.  3x+x3

please guys help me....things are not very clear....they should be pretty simple questions....can u answer it with full working thanks alot
Title: Re: Increasing and Decreasing funcitons....plzz help
Post by: nid404 on September 08, 2009, 02:31:34 pm
Is this AS or A2
Title: Re: Increasing and Decreasing funcitons....plzz help
Post by: Ghost Of Highbury on September 08, 2009, 02:33:32 pm
hey guys can u plzz help me wid this....astarmathsandphysics..neone else...my teacher seemed not to teach me very well
can someone solve these:
find increasing interval of:=
1.  2x3-9x2-24x+7
2.  x4-2x2
3.  3x+x3

please guys help me....things are not very clear....they should be pretty simple questions....can u answer it with full working thanks alot
never done this in add. math

but i can guess that u have to differentiate the function...and express it as greater than 0 and less than 0 to get 2 ranges....
Title: Re: Increasing and Decreasing funcitons....plzz help
Post by: cashem'up on September 08, 2009, 02:38:50 pm
this is AS maths CIE chapter applications of differentiation...plzz somone solve this for me
Title: Re: Increasing and Decreasing funcitons....plzz help
Post by: nid404 on September 08, 2009, 02:41:42 pm
Oh yes it's AS...i'll take a while to do it...if somebody solves it in the meantime then it's fine...or if you can wait i'll solve it in some time
Title: Re: Increasing and Decreasing funcitons....plzz help
Post by: cashem'up on September 08, 2009, 02:49:50 pm
yeah thanks alot..... i will wait....m really confused
Title: Re: Increasing and Decreasing funcitons....plzz help
Post by: nid404 on September 08, 2009, 03:04:26 pm
yeah thanks alot..... i will wait....m really confused
is the ans to the first one 4 and -1...if yes, then i can explain
Title: Re: Increasing and Decreasing funcitons....plzz help
Post by: astarmathsandphysics on September 08, 2009, 03:12:29 pm
Home in 20mins. Will do it then.
Title: Re: Increasing and Decreasing funcitons....plzz help
Post by: nid404 on September 08, 2009, 03:16:56 pm
Ok i guess im correct

1) Differentiate u get
6x2-18x-24
solve the quadratic u get
x=4 0r -1
so x>=4 and x<=-1 is the ans

2) differentiate u get
4x3-4x
4x(x2-1)
so -1<=x<=1

3) differentiate u get
3+3x2
3(1+x2)
f(x) increases with all x values

I hope you got it...I can't really explain maths well...but im pretty confident abt my answers...
Title: Re: Increasing and Decreasing funcitons....plzz help
Post by: nid404 on September 08, 2009, 03:18:46 pm
+ we can wait till astar gets home...he'll be able to explain it well and even confirm my answers if you doubt them...sometimes i doubt my answers...so we better wait and confirm...you needn't worry when astar's there to answer your doubts
Title: Re: Increasing and Decreasing funcitons....plzz help
Post by: slvri on September 08, 2009, 03:23:23 pm
ohk.....to find the interval of increasing or decreasing functions, u first need to differentiate the given function wrt x.
1. d/dx(2x3-9x2-24x+7)=6x2-18x-24
now we have to find the intervals of x for which 6x2-18x-24>0 and also for which 6x2-18x-24<0.
6x2-18x-24=6(x-4)(x+1)
now when x<-1, x-4 is negative, x+1 is negative, expression positive
when -1<x<4,  x-4 is negative, x+1 is positive, expression negative
when x>4, x-4 is positive, x+1 is positive, expression positive
so this expression is increasing over the intervals x<=-1 and x>=4
and decreasing over -1<=x<=4
2. d/dx(x4-2x2)=4x3-4x=4x(x+1)(x-1)
when x<-1, 4x is negative, x+1 is negative, x-1 is negative, expression negative
when -1<x<0, 4x is negative, x+1 is positive, x-1 is negative, expression positive
when 0<x<1, 4x is positive, x+1 is positive, x-1 is negative, expression negative
when x>1, 4x is positive, x+1 is positive, x-1 is positive, expression positive
so this expression is decreasing over the intervals x<=-1 and 0<=x<=1
and increasing over the intervals -1<=x<=0 and x>=1
3. d/dx(3x+x3)=3+3x2=3(x2+1)
since x2+1 is positive for all values of x, this expression is increasing for all values of x (negative infinity<=x<=positive infinity)
sory it took so long.....
Title: Re: Increasing and Decreasing funcitons....plzz help
Post by: astarmathsandphysics on September 08, 2009, 03:40:14 pm
hey guys can u plzz help me wid this....astarmathsandphysics..neone else...my teacher seemed not to teach me very well
can someone solve these:
find increasing interval of F(x):=
1.  2x3-9x2-24x+7
2.  x4-2x2
3.  3x+x3

please guys help me....things are not very clear....they should be pretty simple questions....can u answer it with full working thanks alot
1.Differentiate and solve for x dy/dx>0
6x2-18x-24.0 so x2-3x-4>0 so (x-4)(x+1)>0

Since coefficient of x2 is 1 which is bigger than zero we have a "bum" curve, and (x-4)(x+1)>0 if x>4 or x<-1

or you could say on the interval (4,infinity) the graph increases
(-1,4) the graph decreases
(-infinity,-1) the graph increases

2.Differentiate and solve for x dy/dx>0 4x3-4x>0 4x(x2-1)>0 so4x(x-1)(x+1)>0
The zeroes of the last expresion are at -1,0,1 but since the coefficient of x3 is 4, which is greater than zero, the curve of
4x(x-1)(x+1) tends to infinity as x tends to infinity so on the interval
(1, infinity) the graph increases
(0,1) the graph decreases
(-1,0) the graph increases
(-infinity, -1) the graph decreases
Title: Re: Increasing and Decreasing funcitons....plzz help
Post by: cashem'up on September 08, 2009, 04:01:49 pm
thanks.....phew...finally got it.......owe you guys ...thanks again
Title: Re: Increasing and Decreasing funcitons....plzz help
Post by: nid404 on September 08, 2009, 04:07:11 pm
thanks.....phew...finally got it.......owe you guys ...thanks again

oh glad you got it :)
Title: Re: Increasing and Decreasing funcitons....plzz help
Post by: slvri on September 08, 2009, 04:08:20 pm
thanks.....phew...finally got it.......owe you guys ...thanks again

oh glad you got it :)
me too.... it took me half an hour just to type in the answer
Title: Re: Increasing and Decreasing funcitons....plzz help
Post by: cashem'up on September 08, 2009, 05:57:00 pm
yeah......m so much clear now.....i was so confused.....feels so good....