anonymous
  • anonymous
determine the concavity of the graph of f(x) = 3sin(x)+2(cos(x))^2 at x=pie
Mathematics
katieb
  • katieb
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TuringTest
  • 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
  • anonymous
okay im going to work through it as far as i can when i get stuck ill tell u
anonymous
  • anonymous
derivative of sin is cos right?

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TuringTest
  • TuringTest
yes
TuringTest
  • 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
  • anonymous
when doing the product rule for 2(cos(x))^2 my f(x)= 2x^2 and g(x) is cos(x) right?
TuringTest
  • TuringTest
chain rule, but yes to your substitution chain rule is f(g(x))'=f'(g(x))*g'(x)
anonymous
  • anonymous
okay i got 4(cos(x))^2(-sin(x))
TuringTest
  • 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
  • anonymous
i took the derivative of cosx and the derivative of 2x^2 and then it was 4x(cosx)
TuringTest
  • 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
  • anonymous
oh i see what i did wrong
TuringTest
  • TuringTest
I shouldn't have glossed over that :/
anonymous
  • anonymous
instead of replacing the x in 2x^2 with cosx i just left it alone. so it turn 4cosx
TuringTest
  • TuringTest
exactly
anonymous
  • anonymous
great thanks for being patient in helping me understand that.
TuringTest
  • TuringTest
then times the derivative of cosx...
anonymous
  • anonymous
-4cosxsinx
TuringTest
  • 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
  • anonymous
so i have f'(x) = 3cosx-4cosxsinx
TuringTest
  • TuringTest
and now we gotta do it again this time we will need the product rule for the second term
anonymous
  • anonymous
thats right cause f'(x) gets increase/decrease and f"(x) gets concavity
TuringTest
  • TuringTest
exactly
anonymous
  • anonymous
okay i got -3sin(x)+4sin(x)^2-4cos(x)^2
TuringTest
  • TuringTest
me too :) now plug in x=pi what do you get and what does it say about the concavity there?
anonymous
  • anonymous
should i use a calculator?
TuringTest
  • TuringTest
no it's a special value what's sin(pi) ? cos(pi) ?
TuringTest
  • TuringTest
remember your unit circle...
anonymous
  • anonymous
oh okay yes
anonymous
  • anonymous
pi = 180degrees (1,0) i believe so 0
TuringTest
  • TuringTest
what is zero?
anonymous
  • anonymous
sin(pi)
TuringTest
  • TuringTest
right and cos?
anonymous
  • anonymous
but i meant (-1,0)
TuringTest
  • TuringTest
right
anonymous
  • anonymous
-1
TuringTest
  • TuringTest
so what is the concavity?
anonymous
  • anonymous
concave down
TuringTest
  • TuringTest
right, and the number?
anonymous
  • anonymous
lol let me work through it
anonymous
  • anonymous
-4
TuringTest
  • TuringTest
exactly :D
anonymous
  • anonymous
damn bro god bless you.
TuringTest
  • TuringTest
happy to help :)
anonymous
  • anonymous
lol i have more problems :) id be great if you could help me understand
TuringTest
  • 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
  • anonymous
oh great okay ima post one up right now
TuringTest
  • TuringTest
I mean you should post them separately just to be clear

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