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)
1 answer:
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
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
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Using this set up we can cross out the units that are on opposite sides of the proportion such as miles and hours, leaving us with the desired units of meters and seconds. Then calculate m/s by multiplying 45 by 1000 meters and then dividing that value by 3600 seconds.
The resulting answer is 45mph = 12.5 m/s