finalreview1_soln

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Unformatted text preview: 0001}] 0.0001 0.00005 -0.0001 -0.00005 -0.00005 -0.0001 0.00005 0.0001 -Graphics- And here is the graph really zoomed out: Plot[(x 3)/(Log[1 + x 2]), {x, -10 100, 10 100}] 2 410 210 -110 100 99 295 295 -510 295 -210 -410 295 510 99 110 100 -Graphics- Now we compute derivatives (welcome to quotient rule city): x f [x] 2x4 3x2 - (1+x2 )Log[1+x2 ]2 + Log[1+x2 ] 2x 3x Simplify - (1+x2 )Log[1+x2 ]2 + Log[1+x2 ] " " 2x2 x2 - 1+x2 +3Log[1+x2 ] Log[1+x2 ]2 4 2 Plot the derivative to "estimate" any zeros (it looks like there is one at x = 0): 3x2 2x4 Plot - (1+x2 )Log[1+x2 ]2 + Log[1+x2 ] , {x, -1, 1} 2.2 2...
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