SOLUTION: Sketch by hand F(x) = -2x^3 +6x^2 + 18x -54, including the algebraic calculations of a) x- & y- intercepts b) relative maxima and minima c) points of intersection

Algebra ->  Rational-functions -> SOLUTION: Sketch by hand F(x) = -2x^3 +6x^2 + 18x -54, including the algebraic calculations of a) x- & y- intercepts b) relative maxima and minima c) points of intersection       Log On


   

Question 167060: Sketch by hand
F(x) = -2x^3 +6x^2 + 18x -54, including the algebraic calculations of
a) x- & y- intercepts
b) relative maxima and minima
c) points of intersection
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
+graph%28+300%2C+300%2C+-10%2C+10%2C+-100%2C+100%2C+-2x%5E3+%2B6x%5E2+%2B+18x+-54%29+
a) X-intercepts
Looks like x=3 and x=-3 are intercepts.
Plug those values into the equation and check.
f%28-3%29=-2%28-3%29%5E3+%2B6%28-3%29%5E2+%2B+18%28-3%29+-54
f%28-3%29=54%2B54-54-54=0
f%283%29=-2%283%29%5E3+%2B6%283%29%5E2+%2B+18%283%29+-54
f%283%29=-54%2B54%2B54-54=0
Yes, x=3 and x=-3 are the x-intercepts.
Y-intercept: Set x=0.
f%280%29=-2%280%29%5E3+%2B6%280%29%5E2+%2B+18%280%29+-54
f%280%29=-54
The y intercept is y=-54.
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.
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b) Looks like a relative maxima at x=3, y=0.
Also, looks like a relative minima at x=-1,y=2+6-18-54=-64.
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c) Intersection with what?