Consider the function f: [0, 2π] → R defined by f(x) = sin(x) when 0≤x≤ ²/5 ; when < x ≤ 2π. ax+b A. If function f is continuous on its entire domain, then there are infinitely many pairs of values a and b that would satisfy this continuity requirement. Find an equation in terms of a and b that would provide a defining relation for all such satisfying pairs of values a and b. B. If function f is also differentiable at the point x = 2, then there is only one pair of values a and b that would satisfy this differentiability requirement. Find them.

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