I do not understand the following statements which describe the
First Derivative Test for Local Extrema. 1. If f' changes sign
from positive to negative at c *f' > 0 for x , c and f' < 0 for
x. c), then f has a local maximum value.\ The whole derivative
or the y f' value from the derivative after plugging in c? Or
the derivative equation (started as derived as [I am aware that
is impossible, just bear with me for example sake] 2.If f'
changes sign from negative to positive at c (f' < 0 for x < c
and f' > 0 for x > c,) then f has a local maximum at c. 3. If f'
does not change sign at c (f' has the same sing of both sides of
c), then f has no local extreme value at c. At a left endpoint
a: If f' < 0 (f' > 0) for x > a, then f has a local maximum
(minimum) value at a. At a right endpoint a: If f' < 0 (f'> 0)
for x < b, then f has a local minimum (maximum) value a b.