Question: 7. The graph of a function $f$ is given. Use the graph to estimate the following. Note that the tick marks on the x axis are in intervals of 1, and tick marks on the y axis are in intervals of 2. (a) Find the local maximum and minimum points of the function, as ordered pairs. local maximum $(x, y) = ( )$ (smaller x-value) local maximum $(x, y) = ( )$ (larger x-value) local minimum $(x, y) = ( )$ (smaller x-value) local minimum $(x, y) = ( )$ (larger x-value) (b) Determine the intervals on which the function is increasing and on which the function is decreasing. (Enter your answers using interval notation.) increasing decreasing Graph: red function curve on coordinate axes; local maxima appear at approximately $(-1, 0)$ and $(5, 4)$, and local minima appear at approximately $(-4, -8)$ and $(2, -6)$. Position hint: center

1. **State the problem:** We are given a graph of a function $f$ and need to estimate the local maxima and minima points and determine intervals where the function is increasing or decreasing. 2. **Identify local maxima and minima from the graph:** - Local maxima occur where the function changes from increasing to decreasing. - Local minima occur where the function changes from decreasing to increasing. 3. **From the graph, approximate the points:** - Local maxima at approximately $(-1, 0)$ and $(5, 4)$. - Local minima at approximately $(-4, -8)$ and $(2, -6)$. 4. **Write the local maximum points:** - Smaller $x$-value max: $(-1, 0)$ - Larger $x$-value max: $(5, 4)$ 5. **Write the local minimum points:** - Smaller $x$-value min: $(-4, -8)$ - Larger $x$-value min: $(2, -6)$ 6. **Determine intervals of increase and decrease:** - Increasing intervals are where the function rises as $x$ increases. - Decreasing intervals are where the function falls as $x$ increases. 7. **From the graph:** - Increasing on $(-4, -1)$ and $(2, 5)$ - Decreasing on $(-1 ext{ to }-4)$ (assuming domain extends), $(-1, 2)$, and $(5, 1)$ (assuming domain extends) 8. **Final answers:** - Local maxima: $(-1, 0)$ and $(5, 4)$ - Local minima: $(-4, -8)$ and $(2, -6)$ - Increasing on intervals $(-4, -1)$ and $(2, 5)$ - Decreasing on intervals $(-1, -4)$, $(-1, 2)$, and $(5, 1)$ (assuming domain extends beyond shown graph)