Question

A person's blood pressure P at time t (in seconds) is given by P = 100 + 20cost(6t). Find the maximum value of P (called the systolic pressure) and the minimum value of P (called the diastolic pressure) and give one or two values of t where these maximum and minimum values of P occur.

Answer 1

first find the derivative dP/dt and equate it to zero, then solve for t

Answer 2

So I found the derivative: -120sin6t

Answer 3

So when I set it equal to 0: t = 0, pi/6, pi/3, pi/2... Now what

Answer 4

thats correct

so -120sin(6t) = 0

Answer 5

now you need to find which values of t give maximum and minimum values of P

you can do this by using the second derivative test

Answer 6

So I've derived it a second time and got -720cos6t

Answer 7

I'm just not really sure how to go further from here.

Answer 8

ok now plug in , say, t = pi/6 and see what you get

Answer 9

I think I get 720

Answer 10

yes as cos pi = -1

a positive 2nd derivative indicates a minimum

Answer 11

so at pi/6 the function is a minimum?

Answer 12

yes

Answer 13

and how did you just randomly choose pi/6?

Answer 14

t = pi/3 gives -720 cos 6pi/ 3

Answer 15

why not? the question asked for one or two values of t givibf min or max

Answer 16

lol * giving

Answer 17

pi/3 will give a maximum value as second derivative = -720

Answer 18

So do I just keep doing that for all the values?

Answer 19

0, pi/6, pi/3, pi/2? and so on?

Answer 20

the original function is periodic so there are many peaks and troughs

Answer 21

yes

Answer 22

at what value do I stop though?

Answer 23

you need only find 2 values for P :- plug in pi/6 and pi/3 into the original function

Answer 24

wait, why don't I find values for 0, pi/2?

Answer 25

eg minimum p = 100 + 20 cos 6* PI/6

Answer 26

you can find values for 0 and pi/2 if you want to but the question asks for 1 Or 2

Answer 27

okay i see Thank you!

Answer 28

yw

Answer 29

you should get diastolic 80 and systolic = 120

Answer 30

Got it!