Discussion of Function f

This lecture begins the discussion of the function f(x) = |2x-1| -x²+1 on the domain D(f) = [-3,3], written as a piecewise function. The lecture covers the domain of definition, the image of the function, the continuity of f, finding zeros of the function, and the derivatives of f on the intervals [-3,½[ and [½,3]. The instructor explains the process of finding solutions to the quadratic equation and verifies that the points found are within the given intervals. The lecture emphasizes the importance of checking continuity at critical points and discusses the derivability of f on the closed interval [-3,3] union with {½}. The derivatives of f are calculated on the intervals [-3,½[ and [½,3].