SOLUTION: Hi there. I submitted some problems last Friday, but havent heard anything. If someone has time and is willing to lend soem brain power, I would really appreciate the help. 1.

Algebra ->  Rational-functions -> SOLUTION: Hi there. I submitted some problems last Friday, but havent heard anything. If someone has time and is willing to lend soem brain power, I would really appreciate the help. 1.      Log On


   

Question 55443: Hi there. I submitted some problems last Friday, but havent heard anything. If someone has time and is willing to lend soem brain power, I would really appreciate the help.
1. Consider the function f(x)=2.0x^3 + 4.5x^2. What are the coordinate pairs of the relative maximum and the relative minimum of f(x) in the interval {xI-3 2.In what interval or intervals is the function in problem #1 increasing or decreasing? Use set notation as in question # to indicate the answer.
3. What is the greatest integer less than -10.5?
4. Given that f(x)=x^2+6 and g(x)=x-4, find the composite function f(g(x)).
Thank you for your time.
Angela
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
Hi there. I submitted some problems last Friday, but havent heard anything. If someone has time and is willing to lend soem brain power, I would really appreciate the help.
1. Consider the function f(x)=2.0x^3 + 4.5x^2. What are the coordinate pairs of the relative maximum and the relative minimum of f(x) in the interval {xI-3
F(X)=X^2(2X+4.5).....THE ZEROS ARE X=0...AND 2X+4.5=0...OR..X=-4.5/2=-2.25
IN INCREASING ORDER THEY ARE -2.25 AND 0...
HENCE F(X) IS + VE AND INCREASING FOR X>0
F(X)=0 AT X=0
F(X) IS -VE IN THE INTERVAL (-2.25,0)
F(X)=0 AT X=-2.25
F(X) IS POSITIVE FOR X<-2.25
F'(X)= 6X^2+9X =0......3X(2X+3)=0......2 EXTREMA ARE AT X=0 AND X=-3/2
SEE GRAPH BELOW..F(X) HAS A LOCAL MAXIMUM FOR X IN (-2,0)...
MAXIMUM POINT IS (-3/2 ,27/8)
AND A LOCAL MINIMUM FOR X IN (-1,1)...MINIMUM POINT IS (0,0)
+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2%282%2Ax%2B4.5%29%29+

2.In what interval or intervals is the function in problem #1 increasing or decreasing? Use set notation as in question # to indicate the answer.
ALREADY INDICATED ABOVE
3. What is the greatest integer less than -10.5?
PUT ON NUMBER LINE
-11........-10.5.........-10
HENCE -11 IS THE GREATEST INTEGER LESS THAN -10.5

4. Given that f(x)=x^2+6 and g(x)=x-4, find the composite function f(g(x)).
PUT G(X) =Y =X-4
F(G(X)) = F(Y)= Y^2+6 = (X-4)^2+6=X^2+16-8X+6= X^2-8X+22
Thank you for your time.
Angela