- #1

AnnaSuxCalc

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**Using the Increasing/Decreasing Test **HELP****

## Homework Statement

I have to find the max number of bacteria between t=4 and t=8.5 using the Increasing/Decreasing Test:

(a) Find the largest open intervals (a,b) within the original time interval (4,8.5) during which N'(

*t*)>0 for all t belonging to (a,b) --> during these, N(

*t*) is increasing.

(b) Find the largest open intervals (c,d) within the original time interval (4,8.5) during which N'(

*t*)<0 for all t belonging to (c,d) --> here N(

*t*) is decreasing.

(c) Use (a) & (b) to find the time at which there will be the max number of bacteria.

(d) Use part (c) to find the max number of bacteria.

## Homework Equations

N(

*t*) = 2 + sin

^{2}

*t*- sin

*t*, for 4<t<8.5

## The Attempt at a Solution

OKAY soooo...

First of all I did the derivative of N(

*t*):

N'(

*t*) = sin2

*t*- cos

*t*

Now, I know that for the Increasing/Decreasing Test:

--> if N'(

*t*) is positive on the interval N(

*t*) is increasing there

--> if N'(

*t*) is negative on the interval N(

*t*) is decreasing

My problem seems to always be that I don't know what the question is really asking for, I do not understand (a) & (b)...do I have to find the

__Vertex__here?!??!

I know that once I find (c), the time (

*t*) I just plug that into find N(

*t*), I DON'T plug it into N'(

*t*) right?!

**PLEASE HELP with (a) and (b)**