Assignment 0 - Sample Assignment

Exercise 1 - Derivatives

Calculate the following:

1.1. The first derivative of \(f(t) = t^3\).

1.2. The second derivative of \(f(t) = t^3\).

1.3. Numerically evaluate the second derivative of \(f(t) = t^3\) for \(t=3\).

1.4. If \(t\) represents time (seconds) and \(f\) represents distance of a ball over time (in meters), then what does the second derivative at \(t=3\) mean?

Exercise 2 - Plotting

2.1. Create a plot of the first derivative of \(f(t)\) for the values \(-2 \leq t \leq 1\).

2.2. What does the first derivative of \(f(t)\) for \(t=2\) mean in this case?