Let be a continuous functions satisfying f'( x) = cases 1 & for 0 1 cases and

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

Problem

Let ff be a continuous functions satisfying f′(ln⁡x)={1for 0<x≤1ex−1for x>1f'(\ln x) = \begin{cases} 1 & \text{for } 0 < x \le 1 \\ e^x - 1 & \text{for } x > 1 \end{cases} and f(0)=0f(0) = 0 , then f(x)f(x) can be defined as (1) f(x)={1,if x≤01−ex,if x>0f(x) = \begin{cases} 1, & \text{if } x \le 0 \\ 1 - e^x, & \text{if } x > 0 \end{cases} (2) f(x)={1,if x≤0ex−1,if x>0f(x) = \begin{cases} 1, & \text{if } x \le 0 \\ e^x - 1, & \text{if } x > 0 \end{cases} (3) f(x)={x,if x<0ex,if x>0f(x) = \begin{cases} x, & \text{if } x < 0 \\ e^x, & \text{if } x > 0 \end{cases} (4) f(x)={x,if x≤0ex−1,if x>0f(x) = \begin{cases} x, & \text{if } x \le 0 \\ e^x - 1, & \text{if } x > 0 \end{cases}

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