Mathematics, 18.07.2019 04:30 khollier3119
Find the inflection point of the function. (hint: g''(0) does not exist.) g(x) = 6x|x|
Answers: 1
"
![6[x.\frac{d}{dx} (|x|)+ |x|.\frac{d}{dx} (x)]](/tpl/images/0102/7428/527b6.png)
![6[x.\frac{|x|}{x}+|x|.x ]](/tpl/images/0102/7428/5f341.png)
![6[|x|+|x|.x]](/tpl/images/0102/7428/ec533.png)
![g''(x) = [6.\frac{d}{dx} {|x|+x.|x|}]](/tpl/images/0102/7428/e9aeb.png)
![= 6[\frac{d}{dx}(|x|)+\frac{d}{dx} (x.|x|) ]](/tpl/images/0102/7428/19f9a.png)
![= 6[\frac{|x|}{x} +|x|+x|x|]](/tpl/images/0102/7428/a7fe2.png)
![= 6 |x| [\frac{1+x+x^2}{x} ]](/tpl/images/0102/7428/c6442.png)
is undefined at x=0 because where denominator is "0".
from either side, we find that 
, so really
is undefined. However, we see that 
when 
, and 
when 
, and we know that 
is continuous at 
. This means the concavity must change at 
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Find the inflection point of the function. (hint: g''(0) does not exist.) g(x) = 6x|x|...
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