$9$

Multiple Answer

$1$ point

You are asked to sketch the graph of a continuous function $f$ on $0,6$ satisfying the given properties:

$f^{\text{'}}(1)$ and $f^{\text{'}}(5)$ are undefined.

$f^{\text{'}}(3)=0.$

$f$ has a local maximum at $x=1$ and a local minimum at $x=3.$

$f$ has an absolute maximum at $x=5$ and an absolute minimum at $x=6.$

Without actually sketching the graph, what assumptions can be made about the graph? Choose ALL that apply.

The graph will display a 'corner' where $f^{\text{'}}(x)$ is undefined.

The graph may display a horizontal line at $x=3.$

The absolute minimum $y$ value will be greater than the local minimum $y$ value.

The graph will not be continuous at $x=1$ and $x=4.$

There is insufficient information given to sketch the graph.

The absolute maximum y value will be greater than the local maximum $y$ value.