My question is why create a full table of sign?
Here is a sample question
f(x) = 5x^3 - 3x^5
calculate the coordindates of the stationary points and the nature of
each stationary point.
here is the solution
f'(x) = 15x^2 - 15x^4
f'(x) = 15x^2(1 - x^2)
f'(x) = 15x^2(1+ x)(1 - x)
so the x coordinates of the stationary points are 0, -1 and 1
the stationary points are therefore (-1,-2) , (0,0) and (1,2) so
far so good
now in the example the text book answer draws a table of sign to
determine the nature of the S.P.s
http://i14.tinypic.com/6jq79kp.gif
is there a reason for drawing out the sign for each factor of 15x^2 -
15x^4
ie 15x^2 , (1+ x), (1 - x)
when you can just calculate the sign of f'(x) using 15x^2 - 15x^4
if so, is there a way of determining what the sign of f'(x) is using
the sign of factors?
here is another example where i have drawn of the table of sign
http://i13.tinypic.com/80pwg74.gif
it seems like all positives mean f'(x) is positives and all negatives
mean f'(x) is negative but what about combinations of postives and
negatives
TIA
Doug
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