#10: this graph looks like a polynomial, perhaps a quartic
(4th degree). If you know your classes of functions, they can
help you to solve problems. If it's a quartic, then its
derivative will be cubic -- third degree.
#22: we're still having trouble with algebra, more than
anything, and compositions. In particular, this parenthesis
problem comes up regularly:
$-(x+h)=-x-h$
On #43, any of position, velocity, and acceleration can be
negative or positive. You can't use that as one of your
criteria to decide (unless you're given more information about
that).
Horizontal tangents of functions related to zeros of
derivatives is one way to proceed.
However, once again, symmetry is the best way to proceed....
Last time we continued Section
2.3, using the definition of the derivative to prove
the quotient rule.
Now let's use these rules and see how they make our life better.