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

Christos
 3 years 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

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

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

rulnick
 3 years 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
 3 years 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
 3 years 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
 3 years ago
Best ResponseYou've already chosen the best response.0and decreasing interval*

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