last 1 i need help with today, i promise

[MrRottenTreats]

The measure of effectiveness of a cancer fightning drug is given by e(t)=lnt/6t^2 (t's are the same as x's) where t is the time in months that the patient has been treated and the interval is (0 < or equal to t < or equal to 4. ) When is the treatment most effective.

 

[tkhunny]

't' is not the same as 'x'. Look at them. They are different.

You need to find the maximum value of the function between x = 0 and x = 4. It seems you would need the first derivative to do that. Can you find it?

It's kind of an odd problem statement. Think on cancer treatments. How would this sort of information be used? It took me a minute to think up a rational understanding.

 

[MrRottenTreats]

hmm, i think i can.. you use quotient rule? but then when do i do, plug the intervals in?

 

[tkhunny]

Do you REALLY have no concept of the process whereby the first derivative can be used to find a function maximum or minimum?

1) Find the derivative.
2) Find where it is zero.
3) Is there a solution in the Domain?
4) Check everywhere the derivative doesn't know about (endpoints and corners and things)

You DO get bonus points for coming up with the "quotient rule".

 

[MrRottenTreats]

okay, well i did the deriv and set it to 0;

i got: 0=1-2lnt when i simplified

then i slove for t and then sub that into the original equal along with the points on the interval?

 

[Gene]

You've got it. As long as f(t)>f(0) and f(4) it's a max.