Let g(x) = $\int_0^x {f(t)dt} $, where f is continuous function in [ 0, 3 ] such that ${1 \over 3}$ $ \le $ f(t) $ \le $ 1 for all t$\in$ [0, 1] and 0 $ \le $ f(t) $ \le $ ${1 \over 2}$ for all t$\in$ (1, 3]. The largest possible interval in which g(3) lies is :
$\left[ { - 1, - {1 \over 2}} \right]$
$\left[ { - {3 \over 2}, - 1} \right]$
[1, 3]
$\left[ {{1 \over 3},2} \right]$
Solution
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