Consider the function defined by f(x) = x^2 - ax + 1 x^2 + ax + 1 , 0 < a < 2

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

Consider the function f:(−∞,∞)→(−∞,∞)f: (-\infty, \infty) \to (-\infty, \infty) defined by f(x)=x2−ax+1x2+ax+1,0<a<2.f(x) = \frac{x^2 - ax + 1}{x^2 + ax + 1}, \quad 0 < a < 2. Which of the following is true? (1) (2+a)2f′′(1)+(2−a)2f′′(−1)=0(2+a)^2 f''(1) + (2-a)^2 f''(-1) = 0 (2) (2−a)2f′′(1)−(2+a)2f′′(−1)=0(2-a)^2 f''(1) - (2+a)^2 f''(-1) = 0 (3) f′(1)f′′(−1)=(2−a)2f'(1) f''(-1) = (2-a)^2 (4) f′(1)f′′(−1)=−(2+a)2f'(1) f''(-1) = -(2+a)^2

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