$5\mathrm{.}2\mathrm{.}5$ Exercises

A definite integral starting at $3.$

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Let $g(x)={\displaystyle \underset{0}{\overset{x}{}}}f(t)dt,$ where $f(t)$ is given in the figure below.

$($Click on the graph for a larger version.$)$

Find each of the following:

A$.g(0)=$

B$.g^{\text{'}}(1)=$

C$.$ The interval $($with endpoints given to the nearest $0\mathrm{.}25)$ where $g$ is concave up:

interval $=$

$($Give your answer as an interval or a list of intervals, e$.$g$.,(-$infinity,$8]$ or $(1,5),(7,10),$ or enter nonefor no intervals.$)$

D$.$ The value of $x$ where $g$ takes its maximum on the interval $0x8.$

$x=$