Please check my Algebra
posted by Em .
Determine the maximum possible number of turning points for the graph of the function.
f(x) = 8x^3  3x^2 + 8x  22
I got 2
f(x) = x^7 + 3x^8
I got 7
g(x) =  x + 2
I got 0
How do I graph f(x) = 4x  x^3  x^5?

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