Franklin rockets fly vertically, upwards and downwards, and may change direc- tions repeatedly. It is known that the acceleration of Franklin rockets is a linear function in time, like h′′(t) = at + b, for some values a and b. We don’t know a and b, and we also don’t know what the rockets height h(0) and velocity h′(0) at time t was, but we have observed its height after 1, 2, and 3 seconds. The heights were h(1) = 19, h(2) = 21, and h(3) = 18.
a) What can we say about the average height during the first 3 seconds, if we know that −2 ≤ a ≤ 2?
b) What can be said about the maximum height duri

Question

Franklin rockets fly vertically, upwards and downwards, and may change direc- tions repeatedly. It is known that the acceleration of Franklin rockets is a linear function in time, like h′′(t) = at + b, for some values a and b. We don’t know a and b, and we also don’t know what the rockets height h(0) and velocity h′(0) at time t was, but we have observed its height after 1, 2, and 3 seconds. The heights were h(1) = 19, h(2) = 21, and h(3) = 18.
a) What can we say about the average height during the first 3 seconds, if we know that −2 ≤ a ≤ 2?
b) What can be said about the maximum height duri