SOLUTION: If I was to increase and concave the upward behavior of g(x) then this would be my results: g”(x) <0 & g’(x)>0 Could you tell me if I got the answer correct? Thank you!

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Question 127314: If I was to increase and concave the upward behavior of g(x) then this would be my results:
g”(x) <0 & g’(x)>0 Could you tell me if I got the answer correct? Thank you!

Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
If I was to increase and concave the upward behavior of g(x) then this would be my results:
g”(x) <0 & g’(x)>0 Could you tell me if I got the answer correct? Thank you!
-----------------------
If I understand you correctly, g(x) looks like an exponential function.
The slope is always positive so g'(x)>0.
So g'(x) is always above the x axis and its values are increasing as x increases. I think g'(x) is also an exponential function.
If so g''(x) >0
--------------
Example:
Say g(x)=2^x = e^(xlnx)
Then g'(x) = (lnx)2^x which is also an exponential function.
Therefore g''(x) = lnx(lnx*2^x)+(2^x(1/x)) = 2^x[(lnx)^2+(1/x)]
==========================
Cheers,
Stan H.

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