Consider the function p(x) = ax^5 +bx^4+cx^3+dx^2 + mx +n. Assume that a>0 and that the polynomial has zeros of r(multiplicity 1), s (multiplicity 2), and t(multiplicity 2) where r<s<t.
a) Determine any intervals where P(x)>0
b) Determine any intervals where P(x)<0
c) Determine the number of local maximum points of P(x)
d) Determine the number of local minimum points of P(x)
e) Sketch a possible graph of P(x)
I don't get this question one bit, can someone set me on the path or solve a few of those like a) and d), so I understand them. Plus, just give me a few pointers on how I could start e).