Instructions

Write $up$ your solutions $to$ the following problems paying specific attention $to$ justifying your answer and correct terminology. Show good, relevant mathematics because your score will reflect the correctness $of$ your methods $as$ well $as$ your final answer. Points are $in$ parentheses $at$ the end $of$ the question.

Tasks

Problem $1$:

Determine where the function has any maximums $or$ minimums. Show the analysis that leads $to$ your conclusion. $(5$ points$)$

Problem $2$:

A certain airline requires that rectangular packages carried $onan$ airplane $by$ passengers $be$ such that the sum $of$ the three dimensions $isat$ most $120$ centimeters. Find the dimensions $of$ the square$-$ended rectangular package $of$ greatest volume that meets this requirement.

Include the following $as$ part $of$ your solution

Draw a square$-$ended rectangular package and label all the sides with the variables you choose for the dimensions.

Write $an$ equation that represents the volume $of$ the package

Write $an$ equation that describes the airline's restrictions.

Combine your two equations and apply calculus $to$ determine the dimensions $of$ the package with greatest volume.

Problem $3(5$ points$)$

Print the graph $of$ below $or$ download $to$ a tablet $or$ other device.

Mark each point $on$ the graph where $=0$ with a circle:

Mark each point $of$ inflection $on$ the graph with a triangle:

Scoring

Mark each point $on$ the graph where $f^{\text{'}}(x)=0$ with a circle: @

Mark each point $of$ inflection $on$ the graph with a triangle: $$

Scoring