Let y(t) be a solution of y'=4y(1−y/15). for each of the following initial conditions, state whether y(t) is increasing, decreasing, or constant.
y(0) = 11
y(0) = 15
y(0) = 18

Question

Let y(t) be a solution of y'=4y(1−y/15). for each of the following initial conditions, state whether y(t) is increasing, decreasing, or constant. 
y(0) = 11
y(0) = 15
y(0) = 18

anonymous · Answer

in case you are wondering, I'm going through all the web app questions I wasnt able to answer myself, which was about 6 in 20.

zarkon · Answer

plug in 11,15,18 into y'

zarkon · Answer

what do you get

zarkon · Answer

$$y=11\Rightarrow y'>0$$
$$y=15\Rightarrow y'=0$$
$$y=18\Rightarrow y'<0$$

anonymous · Answer

what allows you to do that? seems insanely easy. .

zarkon · Answer

y'>0...function increasing
y'=0...function constant
y'<0...function decreasing

anonymous · Answer

" plug in 11,15,18 into y' "
did you mean y instead of y' ?

anonymous · Answer

damn.  I just wasted a good amount of time trying to solve the dif eq.

zarkon · Answer

no need

zarkon · Answer

correct...11,15,18 are y values

zarkon · Answer

plugging those in to the differential equation gives you the value of y'

anonymous · Answer

You are correct, sir, and now I get why.

zarkon · Answer

good :)

zarkon · Answer

I'd hope I was correct...I've taught differential equations before ;)

anonymous · Answer

That explains a bit.  Its a web app so I know immediately if its right or not.  which is also why im here - limited feedback from the app.