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| PAGE: 49 | SET: Exercises | PROBLEM: 1 |
A tank holds 
gallons of water.
(a)
The point is 
.
Find the slopes of the secant lines 
.
Consider the point 
.
At 
and the corresponding the value of 
is 
.
So the point is 
.
Slope of the two points is 
.
The slope of the secant line 
is 
.
At 
and the corresponding the value of 
is 
.
So the point is 
.
The slope of the secant line is 
.
At 
and the corresponding the value of is 
.
So the point is 
.
The slope of the secant line is 
.
At 
and the corresponding the value of is 
.
So the point is 
.
The slope of the secant line is 
.
At 
and the corresponding the value of is 
.
So the point is 
.
The slope of the secant line is 
.
The slopes of the secant lines are 
and 
.
(b)
Find the average of the slopes of the secant lines near to 
.
Consider the points are near to 
.
Points are 
and 
.
The slopes of the secant lines are formed from the points 
and 
is 
and 
.
The average of the slopes is 
Therefore the slope of the tangent line at is 
.
(c)
Graph :
Use the values from the table and graph the function.
(1) Draw the coordinate plane.
(2) Plot the points from the table.
(3) Connect the plotted points to a smooth curve.
(4) Draw a approximate tangent line at 
.
From the graph, the green line represents the approximate tangent line at .
So the slope of the tangent line is 
.
(a) The slopes of the secant lines are and .
(b) The slope of the tangent line at is .
(c) The slope of the tangent line after 
minutes is 
.
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