Question

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Answer 1

Part (a)

A function value
`f(a)` is a local maximum if
`f(a)` is the greatest value of
`f` on some open interval containing
`a`. From the graph of
`f`, we see that there are two local maximum values of
`f`: one local maximum is
`\boxed{7}`, and it occurs when
`x=2`; the other local maximum is
`\boxed{6}`, and it occurs when
`x=\boxed{5}`.

• The local maximum is where the graph changes from increasing to decreasing.

Part (b)

A function value
`f(a)` is a local maximum if
`f(a)` is the least value of
`f` on some open interval containing
`a`. From the graph of
`f`, we see that there is one local minimum value of
`f`. The local minimum value is
`\boxed{2}`, and it occurs when
`x=\boxed{4}`.

• The local minimum is where the graph changes from increasing to decreasing.