Question

consider the following function. g(x)= x/1+x^2 determine where the function is concave upward and where it is concave downward.

          consider the following function. g(x)= x/1+x^2 determine where the function is concave upward and where it is concave downward.
        

Added by James R.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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consider the following function. g(x)= x/1+x^2 determine where the function is concave upward and where it is concave downward.
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Transcript

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00:01 We want to identify where function f is concave up versus down.
00:05 The function f of x is x plus 1 over x squared.
00:08 Let's define concavity before moving forward.
00:11 Concave up versus down remember means that f double prime has sign positive or negative for x.
00:15 Thus we have to find f double prime.
00:18 F prime is 1 minus 2 over x cubed and f double prime is 6 over x to the fourth.
00:21 Next we have to separate f f fable prime into intervals based on its critical or partition points...
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