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Mathematics
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Mar 29th, 2015

ROOTS (x-intercepts):

P(x) has 3 real roots:

Z_1 = ( -1, 0)~~~Z_2 = ( 0, 0)~~~Z_3 = ( 1, 0)~~~

SIGN:

P(x) > 0 for x in (- infty,-1)union (0, 1)

P(x) < 0 for x in (-1, 0)union (1, infty)

Local Maxima and Minima:

P(x) has 2 turning points:

E_1 = (  - 1/3sqrt{3} , -0.38)~~~( MIN )~~~E_2 = ( 1/3sqrt{3} , 0.38)~~~( MAX ) ~~~

Increasing/Decreasing Intervals:

P(x) decrease  for x in (- infty, - 1/3sqrt{3} )union (1/3sqrt{3} , infty)

P(x) increase  for x in ( - 1/3sqrt{3} , 1/3sqrt{3} )

Points of Inflection.:

P(x) has one inflection point:

I_1 = ( 0, 0)~~~

Concave Up/Concave Down Intervals:

P(x) is concave up  for x in (- infty,0)

P(x) is concave down  for x in (0, infty)


Mar 29th, 2015

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