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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
 10 months ago
 10 months ago
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
 10 months ago
 10 months ago

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rulnickBest 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.
 10 months ago

ChristosBest ResponseYou've already chosen the best response.0
how did you find the 1/2
 10 months ago

ChristosBest 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
 10 months ago

rulnickBest ResponseYou've already chosen the best response.1
Yes, all were perfect!
 10 months ago

ChristosBest ResponseYou've already chosen the best response.0
so its not decreasing that means its always increasing? Kinda what's the interval?
 10 months ago

ChristosBest ResponseYou've already chosen the best response.0
(0,infinity) increasing?
 10 months ago

rulnickBest ResponseYou've already chosen the best response.1
nondecreasing means increasing or flat. it is flat at the inflection point, increasing everywhere else
 10 months ago

rulnickBest 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)
 10 months ago

ChristosBest 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) ?
 10 months ago

rulnickBest ResponseYou've already chosen the best response.1
yes, very nicely done
 10 months ago

ChristosBest ResponseYou've already chosen the best response.0
and decreasing interval*
 10 months ago

ChristosBest ResponseYou've already chosen the best response.0
like I just say "it's not decreasing anywhere" ?
 10 months ago
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