Question

How do you find and classify all the critical points and then use the second derivative to check your results given `h(t)=-4.9t^2+39.2t+2`?

Answer 1

You first need to find the critical points where `h'(t)=0`, and then check the sign of the second derivative in those points.

Explanation:

Let's calculate first the first derivative `h'(t)=(-4.9)*2*t+39.2`

Hence,

`h'(t)=0` means `-9.8t+39.2=0`, and thus the only critical point is `t=4`.

Let's calculate now the second derivative in `t=4`. But the second derivative is `-9.8` anywhere, so in particular the second derivative in `t=4` is `-9.8`

Since the second derivative is negative in the critical point, the function has a maximum at that point.