12. A function f, continuous everywhere and twice-differentiable for x # A, satisfies f(-...
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12. A function f, continuous everywhere and twice-differentiable for x # A, satisfies ● • f(- √5+¹) = B, f(0) = −1, f (√5-¹) = C, f(A) = 0 • The line y = 2x-1 is a slant asymptote as x → ±∞ • limx A f'(x) = ∞ f'(x) > 0 for x < 0, and for x>1 and x A; f'(x) < 0 for 0<x< 1 √5+1 • f"(x) > 0 for x < -5+¹ and 5¹ < x < A; f"(x) < 0 for 4 5+¹ -√5+1 < x < 5, and x > A. 4 (a) Sketch the graph of f (b) Find constants a, b, c, d for which following is true. The function f(x) Vax³ + bx² + cx+d satisfies the conditions above for suitable real numbers A, B, C. = 12. A function f, continuous everywhere and twice-differentiable for x # A, satisfies ● • f(- √5+¹) = B, f(0) = −1, f (√5-¹) = C, f(A) = 0 • The line y = 2x-1 is a slant asymptote as x → ±∞ • limx A f'(x) = ∞ f'(x) > 0 for x < 0, and for x>1 and x A; f'(x) < 0 for 0<x< 1 √5+1 • f"(x) > 0 for x < -5+¹ and 5¹ < x < A; f"(x) < 0 for 4 5+¹ -√5+1 < x < 5, and x > A. 4 (a) Sketch the graph of f (b) Find constants a, b, c, d for which following is true. The function f(x) Vax³ + bx² + cx+d satisfies the conditions above for suitable real numbers A, B, C. =
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