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

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TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1you'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
 4 years ago
Best ResponseYou've already chosen the best response.0okay im going to work through it as far as i can when i get stuck ill tell u

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0derivative of sin is cos right?

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1this may be handy http://tutorial.math.lamar.edu/pdf/Calculus_Cheat_Sheet_Derivatives_Reduced.pdf chain rule is critical on the next term

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0when doing the product rule for 2(cos(x))^2 my f(x)= 2x^2 and g(x) is cos(x) right?

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1chain rule, but yes to your substitution chain rule is f(g(x))'=f'(g(x))*g'(x)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0okay i got 4(cos(x))^2(sin(x))

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1close, but since you took the derivative of the cos^2 it's just cos to the first power f'(x)=3cosx4cos(x)sin(x)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i took the derivative of cosx and the derivative of 2x^2 and then it was 4x(cosx)

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1yeah 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
 4 years ago
Best ResponseYou've already chosen the best response.0oh i see what i did wrong

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1I shouldn't have glossed over that :/

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0instead of replacing the x in 2x^2 with cosx i just left it alone. so it turn 4cosx

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0great thanks for being patient in helping me understand that.

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1then times the derivative of cosx...

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1sure, 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
 4 years ago
Best ResponseYou've already chosen the best response.0so i have f'(x) = 3cosx4cosxsinx

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1and now we gotta do it again this time we will need the product rule for the second term

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0thats right cause f'(x) gets increase/decrease and f"(x) gets concavity

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0okay i got 3sin(x)+4sin(x)^24cos(x)^2

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1me too :) now plug in x=pi what do you get and what does it say about the concavity there?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0should i use a calculator?

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1no it's a special value what's sin(pi) ? cos(pi) ?

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1remember your unit circle...

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0pi = 180degrees (1,0) i believe so 0

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1so what is the concavity?

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1right, and the number?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0lol let me work through it

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0damn bro god bless you.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0lol i have more problems :) id be great if you could help me understand

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1I'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
 4 years ago
Best ResponseYou've already chosen the best response.0oh great okay ima post one up right now

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1I mean you should post them separately just to be clear
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