Let \( f(x)=\left\{\begin{array}{ll}x+1, & 0 \leq x \leq 1 \\ 2 x^{2}-6 x+6, & 1x \leq 2\end{arr...

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Let \( f(x)=\left\{\begin{array}{ll}x+1, & 0 \leq x \leq 1 \\ 2 x^{2}-6 x+6, & 1x \leq 2\end{array}\right. \) and \( g(t)=\int_{t-1}^{t} f(x) d x \) for \( t \in[1,2] \)
Which of the following hold (s) good?
(a) \( f(x) \) is continuous and differentiable in \( [0,2] \)
(b) \( g^{\prime}(t) \) vanishes for \( t=3 / 2 \) and 2
(c) \( g(t) \) is maximum at \( t=3 / 2 \)
(d) \( g(t) \) is minimum at \( t=1 \)
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