Question

determine the concavity of the graph of f(x) = 3sin(x)+2(cos(x))^2 at x=pie

Answer 1

you're gonna need to find f''(x)
first see how you do finding f'(x)
hint: remember to use the chain rule on 2(cos(x))^2

Answer 2

okay im going to work through it as far as i can when i get stuck ill tell u

Answer 3

derivative of sin is cos right?

Answer 4

yes

Answer 5

this may be handy
http://tutorial.math.lamar.edu/pdf/Calculus_Cheat_Sheet_Derivatives_Reduced.pdf
chain rule is critical on the next term

Answer 6

when doing the product rule for 2(cos(x))^2 my f(x)= 2x^2 and g(x) is cos(x) right?

Answer 7

chain rule, but yes to your substitution
chain rule is
f(g(x))'=f'(g(x))*g'(x)

Answer 8

okay i got 4(cos(x))^2(-sin(x))

Answer 9

close, but since you took the derivative of the cos^2 it's just cos to the first power
f'(x)=3cosx-4cos(x)sin(x)

Answer 10

i took the derivative of cosx and the derivative of 2x^2 and then it was 4x(cosx)

Answer 11

yeah like I tried to amend, your substitution was a little off...
it should actually be
f(x)=2[g(x)]^2
g(x)=cosx

chain rule is
f(g(x))'=f'(g(x))*g'(x)

Answer 12

oh i see what i did wrong

Answer 13

I shouldn't have glossed over that :/

Answer 14

instead of replacing the x in 2x^2 with cosx i just left it alone. so it turn 4cosx

Answer 15

exactly

Answer 16

great thanks for being patient in helping me understand that.

Answer 17

then times the derivative of cosx...

Answer 18

-4cosxsinx

Answer 19

sure, thanks for listening
so you get
f(x)=2[g(x)]^2
g(x)=cosx

chain rule is
[f(g(x))]'=f'(g(x))*g'(x)=4[g(x)]g'(x)=-4cosxsinx
yup :)

Answer 20

so i have f'(x) = 3cosx-4cosxsinx

Answer 21

and now we gotta do it again
this time we will need the product rule for the second term

Answer 22

thats right cause f'(x) gets increase/decrease and f"(x) gets concavity

Answer 23

exactly

Answer 24

okay i got -3sin(x)+4sin(x)^2-4cos(x)^2

Answer 25

me too :)
now plug in x=pi
what do you get and what does it say about the concavity there?

Answer 26

should i use a calculator?

Answer 27

no it's a special value
what's
sin(pi) ?
cos(pi) ?

Answer 28

remember your unit circle...

Answer 29

oh okay
yes

Answer 30

pi = 180degrees (1,0) i believe so 0

Answer 31

what is zero?

Answer 32

sin(pi)

Answer 33

right
and cos?

Answer 34

but i meant (-1,0)

Answer 35

right

Answer 36

-1

Answer 37

so what is the concavity?

Answer 38

concave down

Answer 39

right, and the number?

Answer 40

lol let me work through it

Answer 41

-4

Answer 42

exactly :D

Answer 43

damn bro god bless you.

Answer 44

happy to help :)

Answer 45

lol i have more problems :) id be great if you could help me understand

Answer 46

I've gotta get something to eat at some point, but until/after that I can help.
Just post them and if I'm here I'll help, but others are good at this stuff too.

Answer 47

oh great okay ima post one up right now

Answer 48

I mean you should post them separately just to be clear