Help With this problem!!

[tedog1985]

Philip sackload discovered that the cockroach population in his apartment is described by

N (t) = -t^2 + 18t +880

Where N (t) is the number of cokcroaches in his apartment

and t is the number of cockroaches returned home from vacation


Use the first derivative test to determine

A. The time t when the N (t) reaches a maximum or minimum


b. The maximum N (t)

c. The interval of time t during which th epopulation is increasing.

d. The interval of time t during which the population is decreasing.

E. When will the infestation reach zero?

Thanks for all your guys help!! Im new at this and im kinda loss

 

[galactus]

Try graphing your function so you can see what's going on.

You can see the high point now. That is your maximum. This is achieved when your slope is zero(the tangent line slope is 0). Take the derivative of your function, set to 0 and solve for t.

The other problems can be found by studying the graph and using your function.

 

[tedog1985]

Still not sure where to start to do this!! HELP

 

[stapel]

Still not sure where to start to do this!

Try taking the derivative, setting it equal to zero, and finding the critical point.

Eliz.

 

[tedog1985]

Can someone check this to see if my results are correct. Thanks.



A.

Finding the first derivative and equating to zero we get

N`(t) = -2t +18 =0

-2t = -18

t = 9

At t =9, N(T) reaches maximum.

B.

Maximum N(t) = -81+162 +880 = 961

C.

For t > 9

T = 10

N(T) = -100+180 +880 = 960

T = 8

N(t) = -64+180+880 = 996

Therefore for 0 < t < 9, the population is increasing.

D.

For 9 < t < ∞, the population is decreasing.

E.

Solving N(t) we get

T = -22 , 40

Therefore at t =40, the infestation will reach zero.