Background info This is an Electrical Engineering Signals an

Background info: This is an Electrical Engineering Signals and Systems problem. The textbook being used is \"Engineering Signals and Systems\" by Ulaby and Yagle. We are currently in chapter 2 of that book (https://i.imgur.com/Vv9AxbV.png), so have to solve without Laplace Transform. Please show step by step work/explanation, will thumbs up! Thanks! Compute the impulse response of the LTI system whose step response is shown below

Solution

the given response is the step response.
f(t) = 1 0<t<1.
-1 1<t<2
g(t) step response of a system , then,
impulse response is given by, d/dt (g(t)).
here, g(t) = 1 and -1 for different time regions. but,
d/dt(g(t)) = 0 for both regions. so , impulse response is zer0.