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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