12. A function f, continuous everywhere and twice-differentiable for x # A, satisfies • (-44) = B, f(0) = -1, f() = C, f(A) = 0 • The line y = 2x -1 is a slant asymptote as xto0 • lim, a f'(x) = 00 • f'(x) > 0 for x < 0, and for x > 1 and x # A; f'(x) < 0 for 0< x<1 • "(x) > 0 for x < -4 and A. (a) Sketch the graph of f (b) Find constants a, b, c, d for which following is true. Vax + bx + cx +d satisfies the conditions above for The function f(x) suitable real numbers A, B, C.

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