$(15$ points$)$

The graph below is the graph of the derivative of the function $f(x).$ So$,$ the graph below is the curve $y=f^{\text{'}}(x).$ The domain of $f(x),f^{\text{'}}(x),$ and $f^{\text{'}\text{'}}(x)$ is $f^{\text{'}}(x)f^{\text{'}\text{'}}(x)f(x)(0\mathrm{.}5,2)xxf(x)f(x)(-Q,1)(c,+Q)$

$lb{g}^2-2-2.$ You will need $to$ estimate. You need $to$ justify your answers, $e.g.,by$ sketching a diagram for $f^{\text{'}}(x)$ and for $f^{\text{'}\text{'}}(x).$

Don't forget $to$ instify vour reasenninal

$(a)$ List the intervals $on$ which $f(x)is$ increasing.

$(0\mathrm{.}5,2)$

indeunt $-1$

The Slope $is$ positive and $itis$ above the $x-$axis $so$ a positive $to$ a positive

$(b)$ List the $x$ coordinates where $f(x)$ has local extrema. Indicate whether each $is$ a local maximum $or$ a local minimum.

$(c)$ List the intervals $on$ which $f(x)is$ concave $up.$

$(-Q,1)(c,+Q)$

$lb{g}^2-2$