Question

AP Calculus: The concentration C of a certain chemical in the bloodstream t hours after injection into muscle tissue is given by C=(3t)/(27+t^3) When is the concentration greatest?

Answer 1

take the derivate and set it equal to 0

Answer 2

k, i got \[\frac{ 81-6t }{ (27+t^3)^2 }\]

Answer 3

@TweT226

Answer 4

so set that = 0 and solve for t

Answer 5

how

Answer 6

but it should be 81 - 6t^3

Answer 7

$$C(t)=\frac{3t}{27+t^3}\\C'(t)=\frac{3(27+t^3)-3t(3t^2)}{(27+t^3)^2}=\frac{81+3t^3-9t^3}{(27+t^3)^2}=\frac{81-6t^3}{(27+t^3)^2}\\C'(t_*)=0\\\frac{81-6t_*^3}{(27+t_*^3)^2}=0\\81-6t_*^3=0\\81=6t_*^3\\\frac{27}2=t_*^3\\t_*=\frac3{\sqrt[3]{2}}$$

Answer 8

ooh ok ty ^^

Answer 9

can u help me with another pls? :)