Posted by Em on Tuesday, October 23, 2007 at 4:45pm.
do you know calculus???
first I factored it to
f(x) = -x(x^4 + x^2 - 1)
treating the big bracket as a quadratic, I found x=0, x = ±1.11 and 2 complex roots.
finding the second derivative, setting that equal to zero and solving I got x=0 and x=5/2
so there are two points of inflection, namely at x=0 and at x=5/2
Lastly since the highest power term was negative and an odd exponent, the curve "drops" into the fourth quadrant
so your graph comes down from the second quadrant, crosses at -1.11, comes back up crossing at 0, then comes back down to cross at 1.11. It does a little S bend at x=5/2
You will have to use a different scale for your x and y axes.
BTW, your first two answers are correct
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