SOLUTION: Given the graph of the function y=x^3-3x^2-6x+8, answer the following. All answers must be rounded properly to one decimal place The plotted points on the graph are (1,2) (0.652

Algebra ->  Rational-functions -> SOLUTION: Given the graph of the function y=x^3-3x^2-6x+8, answer the following. All answers must be rounded properly to one decimal place The plotted points on the graph are (1,2) (0.652      Log On


   

Question 1174622: Given the graph of the function y=x^3-3x^2-6x+8, answer the following.
All answers must be rounded properly to one decimal place
The plotted points on the graph are (1,2) (0.652,0)(1.572,0) (3,2) (3.348,0) (2.428,0) (2,-1)
What are the increasing intervals ( , ) U ( , )
and what are the Decreasing intervals ( , ) U ( , )
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
first graph it
+graph%28+600%2C+600%2C+-15%2C+15%2C+-15%2C+15%2Cx%5E3-3x%5E2-6x%2B8%29+
If y’ %28x%29%3E0 then y is increasing (local maximum)
If y’ %28x%29%3C0 then y is decreasing ( local minimum)

y'=3x%5E2-6x-6
find zeros:
3x%5E2-6x-6=0..........simlify, both sides divide by 3
x%5E2-2x-2=0.....use quadratic formula
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a
x=%28-%28-2%29%2B-sqrt%28%28-2%29%5E2-4%2A1%2A%28-2%29%29%29%2F%282%2A1%29
x=%282%2B-sqrt%284%2B8%29%29%2F2
x=%282%2B-sqrt%2812%29%29%2F2
x=%282%2B-sqrt%284%2A3%29%29%2F2
x=%282%2B-2sqrt%283%29%29%2F2.......simplify
x=%28cross%282%29%2B-cross%282%29sqrt%283%29%29%2Fcross%282%29
x=%281%2B-sqrt%283%29%29
solutions:
x=1-+sqrt%283%29 or x=-0.7
x=1%2Bsqrt%283%29 or x=2.7


the increasing intervals (-infinity ,-0.7+) U (2.7 ,infinity )
the Decreasing intervals ( -0.7,0 ) U (0,2.7 ) or simply ( -0.7,2.7 )