- anonymous

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

- katieb

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- TuringTest

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

- anonymous

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

- anonymous

derivative of sin is cos right?

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## More answers

- TuringTest

yes

- TuringTest

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

- anonymous

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

- TuringTest

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

- anonymous

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

- TuringTest

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)

- anonymous

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

- TuringTest

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)

- anonymous

oh i see what i did wrong

- TuringTest

I shouldn't have glossed over that :/

- anonymous

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

- TuringTest

exactly

- anonymous

great thanks for being patient in helping me understand that.

- TuringTest

then times the derivative of cosx...

- anonymous

-4cosxsinx

- TuringTest

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 :)

- anonymous

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

- TuringTest

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

- anonymous

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

- TuringTest

exactly

- anonymous

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

- TuringTest

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

- anonymous

should i use a calculator?

- TuringTest

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

- TuringTest

remember your unit circle...

- anonymous

oh okay
yes

- anonymous

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

- TuringTest

what is zero?

- anonymous

sin(pi)

- TuringTest

right
and cos?

- anonymous

but i meant (-1,0)

- TuringTest

right

- anonymous

-1

- TuringTest

so what is the concavity?

- anonymous

concave down

- TuringTest

right, and the number?

- anonymous

lol let me work through it

- anonymous

-4

- TuringTest

exactly :D

- anonymous

damn bro god bless you.

- TuringTest

happy to help :)

- anonymous

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

- TuringTest

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.

- anonymous

oh great okay ima post one up right now

- TuringTest

I mean you should post them separately just to be clear

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