In the CSET math test prep book published by Research and Education
Association, the following problem is posed and solved:
For which of the following intervals is the graph of y = x^4 - 2x^3 -
12x^2 concave down? (-2, 1); (-1, 2); (-1, -2); (- infinity, -1).
The solution reads:
y = x^4 - 2x^3 - 12x2
y' = 4x^3 - 6x^2 - 24x
y'' = 12x^2 - 12x - 24, = 12(x-2)(x+1), therefore the interval (-1, 2)
is the correct answer.
What do the signs (') and ('') mean, and how are the authors moving
from one equation to the next?
Thanks in advance,
Henrysun909
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