2) Given the function: f(x) = x5 – 7x4 + 24x3 – 32x + 64
a) Describe the end behavior.
b) How many at most turning points are there for the function?
c) How many at most roots are there for the function?
d) Find all the zeros of f(x), real and non-real, assuming that one zero is 2 + 2i.
e) Show the function in factored form using the answers you got from part (b).
f) Sketch a graph of the function.