#### Passage II (Q

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

#### Passage II (Q. Nos. 91 to 94) Let ff be a function that is differentiable everywhere and that has the following properties : - f(x)>0f(x) > 0 - f′(0)=−1f'(0) = -1 - f(−x)=1f(x)f(-x) = \frac{1}{f(x)} and f(x+h)=f(x)⋅f(h)f(x+h) = f(x) \cdot f(h) A standard result is ∫f′(x)f(x)dx=log⁡∣f(x)∣+C\int \frac{f'(x)}{f(x)} dx = \log |f(x)| + C . If h(x)=f′(x)h(x) = f'(x) , then h(x)h(x) is given by (1) −f(x)-f(x) (2) 1f(x)\frac{1}{f(x)} (3) f(x)f(x) (4) ef(x)e^{f(x)}

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