Question

function P(x) = x4 − x3 − 11x2 + 9x + 18. Describe to the CEO what the graph looks like and, in general, how to sketch the graph without using technology. Use complete sentences, and focus on the end behaviors of the graph and where the company will break even (where P(x) = 0). (10 points)

Answer 1

4th degree, so the ends both point in same direction
positive leading coefient so both ends point up

factor it to see wheere the roots are
the roots are r1,r2,r3,r4 in P(x)=(x-r1)(x-r2)(x-r3)(x-r4)
factor
P(x)=(x-3)(x-2)(x+1)(x+3)
the roots are
3,2,-1,-3

disregard negative roots becasue you can't have negative time or something
3 or 2

see my rough graph

here is rough scetch