What is this question asking?
So far I've got An Inflection Point is where a curve changes from Concave upward to Concave downward (or vice versa) The second derivative tells us if the slope increases or decreases.
• When the second derivative is positive, the function is concave upward.
• When the second derivative is negative, the function is concave downward.
Could an example of this be looking at the economy over time?
Best Answer
Let $c(t)$ represent the distance travelled by a car at time $t$ on a straight road. Suppose $c(t)$ is strictly monotonic on some interval $[t_0-s,t_0+s]$ with $s>0$ and that $c''(t_0)=0.$ Then as $t$ increased from $t_0-s$ to $t_0$, the velocity, which is positive for $t\in [t_0-s,t_0),$ decreased to the local minimum velocity $c'(t_0)$, and as $t$ increased from $t_0$ to $t_0+s$ the velocity increased. In particular if $c'(t_0)=0$ then the car slowed to a stop and then accelerated in the same direction. Example :$c(t)=t^3,$ with $t_0=0.$