The discussion focuses on determining the constants K and M for the piecewise function h(x) defined as h(x) = kx² + 1 for 0 < x ≤ 2 and h(x) = mx - 3 for 2 < x ≤ 5, ensuring that h is differentiable at x = 2. To achieve differentiability, two conditions must be satisfied: continuity at x = 2, represented by the equation \lim_{x \to 2^-} h(x) = \lim_{x \to 2^+} h(x), and differentiability, represented by \lim_{x \to 2^-} h'(x) = \lim_{x \to 2^+} h'(x). Solving these equations will yield the values of K and M.
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