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!

Algebra ->  Rational-functions -> 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!       Log On


   

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) About Me  (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!
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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
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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)]
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Cheers,
Stan H.