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Increasing and Decreasing funcitons....plzz help

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slvri:
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.....

astarmathsandphysics:

--- Quote from: ima_shah2002 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

--- End quote ---
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

cashem'up:
thanks.....phew...finally got it.......owe you guys ...thanks again

nid404:

--- Quote from: ima_shah2002 on September 08, 2009, 04:01:49 pm ---thanks.....phew...finally got it.......owe you guys ...thanks again

--- End quote ---

oh glad you got it :)

slvri:

--- Quote from: nid404 on September 08, 2009, 04:07:11 pm ---
--- Quote from: ima_shah2002 on September 08, 2009, 04:01:49 pm ---thanks.....phew...finally got it.......owe you guys ...thanks again

--- End quote ---

oh glad you got it :)

--- End quote ---
me too.... it took me half an hour just to type in the answer

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