If \( f(x)=\left\{\begin{array}{cl}e^{x}, & 0 \leq x \leq 1 \\ 2-e^{x-1}, & 1x \leq 2 \\ x-e, & ... VIDEO
If \( f(x)=\left\{\begin{array}{cl}e^{x}, & 0 \leq x \leq 1 \\ 2-e^{x-1}, & 1x \leq 2 \\ x-e, & 2x \leq 3\end{array}\right. \) and \( g(x)=\int_{0}^{x} f(t) d t \)
\( x \in[1,3] \) then \( \quad \) [More than One Correct Option, 2006]
(a) \( g(x) \) has local maxima at \( x=1+\log _{e} 2 \) and local minima at \( x=e \)
(b) \( f(x) \) has local maxima at \( x=1 \) and local minima at \( x=2 \)
(c) \( g(x) \) has no local minima
(d) \( f(x) \) has no local maxima
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