Thread: When is the concentration greatest?

The concentration C of insulin in the bloodstream t hours after injection into muscle tissue is

C(t)=4t/2+t^3

When is the concentration greatest? t=?

take the derivative of C w/r to time, set C'(t) = 0 and solve for critical value(s) of t, then use the 1st derivative test to check which critical value(s) yields a minimum.

Originally Posted by skeeter

take the derivative of C w/r to time, set C'(t) = 0 and solve for critical value(s) of t, then use the 1st derivative test to check which critical value(s) yields a minimum.

Could you help me get the derivative

this derivative is fairly basic ... use the quotient rule and show what you get for a derivative.

Originally Posted by skeeter

this derivative is fairly basic ... use the quotient rule and show what you get for a derivative.

Is this right? (2+t^3)[4t]-(4t)[2+t^3]
(2+t^3)(4)-(4t)(3t^2)
(8t^3)-(12t^3)
-4t^3

no

S.O.S. Mathematics CyberBoard :: View topic - When is concentration greatest?

Originally Posted by skeeter

no

S.O.S. Mathematics CyberBoard :: View topic - When is concentration greatest?

What do I do with 8-8t^(3)/ (2+t^3)^2

Originally Posted by bgwarhawk

What do I do with 8-8t^(3)/ (2+t^3)^2

*Cough*

Originally Posted by skeeter

take the derivative of C w/r to time, set C'(t) = 0 and solve for critical value(s) of t, then use the 1st derivative test to check which critical value(s) yields a minimum.

So solve etc.

Originally Posted by mr fantastic

*Cough*


So solve etc.

How do I get t= if I get t^3=1???

Originally Posted by bgwarhawk

How do I get t= if I get t^3=1???

cube root...

What do I do with the 1?

Originally Posted by bgwarhawk

What do I do with the 1?

Originally Posted by skeeter

take the derivative of C w/r to time, set C'(t) = 0 and solve for critical value(s) of t, then use the 1st derivative test to check which critical value(s) yields a minimum.

t = 1 is the critical value in this case and you are checking if there is a maximum. But the idea is the same.