Question

Determine the point of inflection, p(t)= 20 / (1+3e^-0.02t)

Answer 1

You need to find the 2nd derivative

Answer 2

yea i need help with that.

Answer 3

Ok can you find the first derivative?

Answer 4

nope.

Answer 5

just integrate the 2nd dericative to get to the 1st derivative :)

Answer 6

Do you know the quotient rule?

Answer 7

i get confused with the d/dx of the e functions

Answer 8

yes i do

Answer 9

\[\frac{d}{dx}(e^{at})=(at)'e^{at}=ae^{at} \text{ where } a \text{ is a constant }\]

Answer 10

so d/dx of (1+3e^-0.02t) is: -0.02(3e^-0.02t)?

Answer 11

\[p'=\frac{(20)'(1+3e^{-0.02t})-20(1+3e^{-0.02t})'}{(1+3e^{-0.02t})^2}\]
Yes!

Answer 12

so is the first derivative

Answer 13

0.4(3e^-0.02t)/(1+3e^-0.02t)^2

Answer 14

yes

Answer 15

Then you can multiply 3 and .4

Answer 16

okay, now can we go thru the second derivative together?,

Answer 17

1.2e^-0.02t?

Answer 18

Again you will need to use quotient rule

Answer 19

You will need the chain rule to for the bottom and for the e thing

Answer 20

i tried, and its not working

Answer 21

\[p''=\frac{(1.2e^{-0.02t})'(1+3e^{-0.02t})^2-(1.2e^{-0.02t})((1+3e^{-0.02t})^2)'}{(1+3e^{-0.02t})^2}\]

Answer 22

isnt the denominator to the power 4?

Answer 23

yes that is a type-o

Answer 24

ok

Answer 25

okay

Answer 26

now can we go thru the steps?

Answer 27

for the quotient rule?

Answer 28

all i did was do [(top)'(bottom)-(top)(bottom)'] /(bottom)^2

Answer 29

i meant for this question

Answer 30

so is it? 0.024e^-0.02t(bottom) - top(2)(1+3e^-0.02t)(1.2e^-0.02t)

Answer 31

oops sorry not 1.2e, i meant 0.06e^...

Answer 32

\[(1.2)(-0.02)e^{-0.02t}=(1.2e^{-0.02t})'\]

Answer 33

\[2(1+3e^{-0.02t})(0+3(-0.02)e^{-0.02t})=((1+3e^{-0.02t})^2)'\]

Answer 34

Just plug in

Answer 35

this is what i got as my final answer:
(0.024e^-0.02t(1-6(1+3e^-0.02t))/ (1+3e^-0.02t)^3