*We want to find the ticket price that gives the maximum profit, and also find that maximum profit.*

Find a reasonable domain and range for this situation.

Area depends on length and width – which makes sense.

Let’s get the vertex for \(A\left( w \right)=w\left( \right)\) both algebraically and using a Graphing Calculator: To get the vertex, we can use (\(\displaystyle -\frac\), plug \(\displaystyle -\frac\) into the \(w\) to get the \(y\)) to find the coordinates of the vertex, when \(y=a bw c\): \(\displaystyle y=w\left( \right)\,\,\,\,\,\,\,\text\,\,\,\,\,\,y=-2 120w\) \(\displaystyle -\frac=-\frac=\,\,\,\,30\, \text\) (This is the width, and to get the length, we plug this into \(120-2w\), and get (maximum), moved the cursor to the left of the top after “Left Bound?

Note also that we will discuss Optimization Problems using Calculus in the Optimization section here.

where \(t\) is the time in seconds, and \(h\) is the height of the ball.

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