Determine the points of discontinuity of the function f and the nature of discontinuity at each of those points:

Also check whether the function f is derivable at x = 1.

To find the points of discontinuity in the given piecewise function, we need to examine the boundary points for each piece and determine whether the function is continuous at these boundaries. The function is defined as follows:

\[f(x) = \begin{cases}
    -x^2 & \text{when } x \leq 0 \\
    4 - 5x & \text{when } 0 < x \leq 1 \\
    3x - 4x^2 & \text{when } 1 < x \leq 2 \\
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