The function is $\"\"$ , where $\"\"$ is time in seconds and $\"\"$ is the height in feet.

(a)

Graph the height of the ball.

Graph of the function $\"\"$ is :

$\"\"$

(b)Find the greatest height reached by the ball:

Observe the graph:

$\"\"$ has an absolute maximum $\"\"$ at $\"\"$ .

Support numerically :

Construct the table by using the values of $\"\"$ .

Choose t values in small intervals on either side of the estimated t-value for the maximum.

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

$\"\"$	$\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$

Observe the table:

Because $\"\"$ and $\"\"$ , there is a relative maximum in the interval $\"\"$ .Therefore, the greatest height reached by the ball is $\"\"$ or about $\"\"$ .

(a)

Graph of the function $\"\"$ is :

$\"\"$ .

(b) The greatest height reached by the ball is $\"\"$ or about $\"\"$ ft.