Question

For some positive constant C, a patient's temperature change, T, due to a dose, D, of a drug is given by T=(C/2−D/3)*D^2.
What dosage maximizes the temperature change?
D=

The sensitivity of the body to the drug is defined as dT/dD. What dosage maximizes sensitivity?
D=

Answer 1

@mathmale @ganeshie8

Answer 2

So many letters here

Answer 3

C is a constant
T is a function of D

Answer 4

Yes

Answer 5

do you know the standard method to find the mex/min values of some function ?

Answer 6

take the derivative and set it to 0?

Answer 7

Yes, do it

Answer 8

start by finding the first derivative of T

Answer 9

\[\frac{ d(3c-2d) }{ 3 }+d ^{-1/3}\]

Answer 10

?

Answer 11

looks wrong

Answer 12

sorry i just had a calc exam 5 hours ago and got 2 hours of sleep last night so im exhausted. But of course, my professor had to assign homework due the day after the test

Answer 13

its easy, just expand and take the derivaitve :

T=(C/2−D/3)*D^2
= (C/2)D^2 - (1/3)D^3

T' = CD - D^2

Answer 14

wait the page just refreshed and says its now due Sunday :D. I'll finish this problem with you then hit the sack so i can get a goodnight sleep tonight

Answer 15

ahh that calc test must have been hard... thats okay :)

Answer 16

it was very hard. I think i bombed the test ;(

Answer 17

haha how sure are you

Answer 18

like pretty sure

Answer 19

does it count too much in the final grade ?

Answer 20

not as the midterm and final, i still have a chance at a low b but we will see how the next test goes

Answer 21

ahh then no big deal, past is past... you can always prepare well for the future tests... cheer up :)

Answer 22

see if you can finish rest of the problem
it should be simple if you know what you're doing..

Answer 23

is it \[D=\sqrt{CD}\]

Answer 24

T' = CD - D^2

right ?

Answer 25

yeah

Answer 26

setting that equal to 0 gives

CD - D^2 = 0

D(C - D) = 0

D = 0 or D = C

Answer 27

zero dosage makes not much sense

Answer 28

didn't think about doing it that way

Answer 29

so D = C must be the maximum

Answer 30

okay

Answer 31

for part b, you need to find the value of D that maximizes the T'

Answer 32

same thing,
differentiate T'

Answer 33

you mean take the second derivative?

Answer 34

T' = CD - D^2

T'' = ?

Answer 35

T'' is the first derivative of T' and the second derivaitve of T

Answer 36

-2D? or -2D+C?

Answer 37

T' = CD - D^2

T'' = C - 2D

Answer 38

ok I thought it was the second one but wasn't sure

Answer 39

D=C/2

Answer 40

looks good!

Answer 41

Thanks man, Im gonna head to bed and finish this homework on a fresh head :D

Answer 42

have good sleep :)