[Math] Finding average speed using Calc

Question

Hey I've been trying to solve this problem for a while now as review for a final coming up. Here's the problem
I've solved part a) for 1 and 3 seconds, but I'm stuck on b). My take was to solve for when the derivative equals 0 which I did above, and then use that to find the slope, but I don't think that works. Any help on how to solve this would be greatly appreciated

Answer 1

As stated, problem 2 has nothing to do with derivatives: you just want the average rate of change of $h$ on $[a,b]$ which is $\frac{h(b)-h(a)}{b-a}$. Part of the point of calculus is that if $b$ is very close to $a$ then this is very nearly $h'(a)$. This problem is a concrete way of investigating what "very close" means for a particular function, namely $h$, near a particular point, namely $2.5$.