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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)union (1, infty)

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

Local Maxima and Minima:

P(x) has 3 turning points:

E_1 = ( -1/8 - 1/8sqrt{17} , -0.62)~~~( MIN )~~~E_2 = ( -1/8 + 1/8sqrt{17} , 0.2)~~~( MAX ) ~~~E_3 = ( 1, 0)~~~( MIN )~~~

Increasing/Decreasing Intervals:

P(x) decrease  for x in (- infty,-1/8 - 1/8sqrt{17} )union (-1/8 + 1/8sqrt{17} , 1)

P(x) increase  for x in (-1/8 - 1/8sqrt{17} , -1/8 + 1/8sqrt{17} )union (1, infty)

Points of Inflection.:

P(x) has 2 inflection points:

I_1 = ( 1/4 - 1/12sqrt{33} , -0.27)~~~I_2 = ( 1/4 + 1/12sqrt{33} , 0.09)~~~

Concave Up/Concave Down Intervals:

P(x) is concave up  for x in (- infty,1/4 - 1/12sqrt{33} )union (1/4 + 1/12sqrt{33} , infty)

P(x) is concave down  for x in (1/4 - 1/12sqrt{33} , 1/4 + 1/12sqrt{33} )


As x-approaches to infinity f(x) approaches to infinity on positive side

As x-approaches to infinity f(x) approaches to infinity on negative side

Mar 29th, 2015

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