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 Here are the plotted points on the graph: (-0.732

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 Here are the plotted points on the graph: (-0.732      Log On


   

Question 1174623: 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
Here are the plotted points on the graph: (-0.732, 10.392) (-2, 0) (1,0) (4,0) (2.732,-10.392)
what is the relative min, and what is the relative maximum?
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+
A relative maximum point is a point where the function changes direction from increasing to decreasing (making that point a "peak" in the graph).
Similarly, a relative minimum point is a point where the function changes direction from decreasing to+increasing (making that point a "bottom" in the graph).
If f%28x%29 has a relative extrema at x=c and f′%28c%29 (or y′%28c%29 ) exists then x=c is a critical point of f%28x%29. In fact, it will be a critical point such that f′%28c%29=0
find y′
y′=3x%5E2-6x-6+
find
3x%5E2-6x-6=0 ........simplify, 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=1-+sqrt%283%29
x=1%2Bsqrt%283%29
Extreme Points of y=x%5E3-3x%5E2-6x%2B8 are:
Maximum at (1-+sqrt%283%29, 6+sqrt%283%29) or (-0.7, 10.4)
Minimum at (1%2Bsqrt%283%29, -6sqrt%283%29) or (2.7,+-10.4)