# The number of miligrams x of a medication in the bloodstream t hours after a dose is taken can be modeled byx(t)= 2000t/t^2+16(a) For what t-values is x increasing?(b) Find the t-value at which s is maximum.(c) Fine the maximum value of x.

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The number of miligrams x of a medication in the bloodstream t hours after a dose is taken can be modeled by

x(t)= 2000t/t^2+16

(a) For what t-values is x increasing?

(b) Find the t-value at which s is maximum.

(c) Fine the maximum value of x.

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Step 1

we are given a function

Step 2

Now, we will find derivative and then we can set derivative to 0

and then we can solve for t

and then we find point  and time can never be negative

so, we will only consider t=4 help_outlineImage Transcriptionclose2000 dr t16 x'(t) 2000 dtt16 d 0(F+16) ( +16)t dt -2000. dt (P+16) 2000. 1-(16)-2ft (+16) 2000 (-r16) x'(t (P+16) 2000(-16) (r+16) t-4,t 4 x(4) =2000(4) 42+16 x(4) 250 fullscreen
Step 3

Now, we can draw a number line and locate t=4

and then we can find sign of derivative on each intervals ...

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### Derivative 