Determine impulse resonse of First Order Hold (FOH)
Hint:

$f(t)$ is the expected output after passing a sampled function through the first order hold function with impulse response $h_{FOH}(t)$. 

The sampled function is $f(kh)$, with $k$ being the sample index and $h$ being the sample interval, with zeros elsewhere as a continuous time process. The output is the continuous-time convolution of $f(kh)$ with $h_{FOH}(t)$.  In the first-order hold, $h$ is also the duration of the hold time, so spanning one sample interval.

If $f(kh) = \delta(0)$, with $k=0$, which is the unit impulse at time $t=0$, the result should be the impulse response, $h_{FOH}(t))$.