Answer
a) If $f'(x)>0$ on an interval, then $f$ is increasing on that interval. If $f'(x)<0$ on an interval, then $f$ is decreasing on that interval.
b) To say that $f$ is concave upward on an interval $I$ is to say that the graph of $f$ lies above all of its tangents on $I$.
c) If $f''(x)>0$ for all $x$ in $I$, then the graph of $f$ is concave upward on $I$. If $f''(x)<0$ for all $x$ in $I$, then the graph of $f$ is concave downward on $I$.
d) Inflection points are any point $P$ on a curve $y=f(x)$ where $f$ is continuous there and the curve changes from concave upward to concave downward or vice versa at $P$.
