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Christos
Group Title
f(x) = (2x +1)^3
f'(x) = 6(2x + 1)^2
f''(x) = 48x + 24
I need to know when its concave up/down increasing /decreasing and the inflection points I am new to this kind of stuff
 one year ago
 one year ago
Christos Group Title
f(x) = (2x +1)^3 f'(x) = 6(2x + 1)^2 f''(x) = 48x + 24 I need to know when its concave up/down increasing /decreasing and the inflection points I am new to this kind of stuff
 one year ago
 one year ago

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rulnick Group TitleBest ResponseYou've already chosen the best response.1
First derivative is nonnegative for all real x, so f is nondecreasing. Second derivative is everywhere matching the sign of x+1/2, so there is an inflection point at x=1/2. The function is concave down on x<1/2 and concave up on x>1/2.
 one year ago

Christos Group TitleBest ResponseYou've already chosen the best response.0
how did you find the 1/2
 one year ago

rulnick Group TitleBest ResponseYou've already chosen the best response.1
f''(x)=0 at x=1/2
 one year ago

Christos Group TitleBest ResponseYou've already chosen the best response.0
Ok and something more are my derivative calculations correct? f(x) = (2x +1)^3 f'(x) = 6(2x + 1)^2
 one year ago

rulnick Group TitleBest ResponseYou've already chosen the best response.1
Yes, all were perfect!
 one year ago

Christos Group TitleBest ResponseYou've already chosen the best response.0
so its not decreasing that means its always increasing? Kinda what's the interval?
 one year ago

Christos Group TitleBest ResponseYou've already chosen the best response.0
(0,infinity) increasing?
 one year ago

rulnick Group TitleBest ResponseYou've already chosen the best response.1
nondecreasing means increasing or flat. it is flat at the inflection point, increasing everywhere else
 one year ago

rulnick Group TitleBest ResponseYou've already chosen the best response.1
so increasing on the entire real line except at 1/2, where it is flat (deriv=0)
 one year ago

Christos Group TitleBest ResponseYou've already chosen the best response.0
here it asks me the open interval on which f is increasing what should I put? (inf,1/2)U(1/2,int) ?
 one year ago

rulnick Group TitleBest ResponseYou've already chosen the best response.1
yes, very nicely done
 one year ago

Christos Group TitleBest ResponseYou've already chosen the best response.0
and decreasing interval*
 one year ago

Christos Group TitleBest ResponseYou've already chosen the best response.0
like I just say "it's not decreasing anywhere" ?
 one year ago

Christos Group TitleBest ResponseYou've already chosen the best response.0
Alright, thank you!
 one year ago
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