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 one year 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
 one year 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

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rulnick
 one year ago
Best ResponseYou've already chosen the best response.1First 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.

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

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

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

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

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

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

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

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

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

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