Question

HELP

Answer 1

Find the second derivative.

Answer 2

okay ill try, im not that good at it and i just learned it today

Answer 3

what is your first derivative?

Answer 4

2(t+1)

Answer 5

You're not showing your work, so I have no idea what you're trying to do

Answer 6

You have to first find \(dy/dx\)

Answer 7

It's very easy because you are just undoing the integral

Answer 8

i dont know how thats why i put up the question, thats why i asked for someone to explain it, it is a ractice problem and i compare the steps when i do the rest of my homework if i need help @wio

Answer 9

Well FTC says: \[
\frac{d}{dx}\left(\int_c^x f(t)~dt\right) = f(x)
\]

Answer 10

That is why: \[
\frac{dy}{dx} = \frac{d}{dx}\left(\int_0^x\frac{6}{1+2t+t^2} dt\right) = \frac{6}{1+2x+x^2}
\]

Answer 11

Function is concave up when \(\frac{d^2y}{dx^2} >0 \)

Answer 12

So you have to take the derivative another time

Answer 13

@TuringTest can you please continue??

Answer 14

is that what you got for the derivative of\[\frac6{(1+t^2)}\]?

Answer 15

second derivative or first?

Answer 16

im pretty sure ive been ding it all wrong, wanna start all over?

Answer 17

yes, let's

Answer 18

right, so what is the derivative of that?

Answer 19

no, how did you get that?

Answer 20

oh wait! i was doing the equation for my last problem ,is it -12/(x+1)^3

Answer 21

yes! very good

Answer 22

:)

Answer 23

well that was easy
nice job :)

Answer 24

oh wait, thats it? hahah

Answer 25

thats the interval?

Answer 26

interval? oh lol I guess we are not done, my bad
what is the condition on f(x) where it is concave up?

Answer 27

what feature does its second derivative have where it is concave up?

Answer 28

im not sure..:/

Answer 29

@TuringTest

Answer 30

f(x) is concave up is when the second derivative is greater than zero
f(x) is concave down when the second derivative is less then zero
f(x) has an inflection point where the second derivative equals zero

Answer 31

where?

Answer 32

oh wait it is concave down because it is negative... missed that

Answer 33

let me rephrase
f(x) is concave up is where the second derivative is greater than zero
f(x) is concave down where the second derivative is less then zero
f(x) has an inflection point where the second derivative equals zero

Answer 34

you need to determine for which values of x you have f''(x) > 0

Answer 35

yes and isnt the second derivative less than 0???

Answer 36

no, it has a variable in it
is -x < 0 ???
not if x is negative...

Answer 37

is this a trick question..

Answer 38

you need to find for which values of x you have\[{-12\over(1+x)^3}>0\]

Answer 39

where did o uget 6/(1+x)^3 from?

Answer 40

from being a dummy, sorry :P

Answer 41

hahaha its fine i just got confised

Answer 42

can you explain it? i realy dont know

Answer 43

@TuringTest

Answer 44

this is a random graph

Answer 45

you want to find this intervalwhich you can do by finding where the second derivative is positive, i.e. where\[{-12\over(x+1)^3}>0\]