The Tangent to a Curve

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The Tangent to a Curve
Select some point on the parabola arbitrarily
close to (1, 1).
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The Tangent to a Curve
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The Tangent to a Curve
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The Tangent to a Curve
In order to find this tangent line to the point
(1, 1) we need to find the slope of the line.
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The Tangent to a Curve
Select values for x getting closer to 1.
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The Tangent to a Curve
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The Tangent to a Curve
8
The Tangent to a Curve
Suppose that a ball is dropped from the upper
observation deck of the CN Tower, 450 m above the
ground. Find the velocity of the ball after 5
seconds.
Compute s over brief period of time.
Check for intervals from 5 sec.to 6, 5.1, 5.05,
5.01, 5.001.
Average velocity compared to the instantaneous
velocity
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The Tangent to a Curve
Compute the slopes of the secant lines between
each pair of points. A. x1, x5 B. x1, x4
C. x1, x3 D. x1, x2
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The Tangent to a Curve
If an arrow is shot upward on the moon with a
velocity of 58 m/s, its height in meters after t
seconds is given by
Find the average velocity over the given time
intervals
1, 2, 1. 1.5, 1, 1.1, 1,
1.01, 1, 1.001
Find the instantaneous velocity after 1 second.
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The Tangent to a Curve
The position of a car is given by the values in
the table.
Find the average velocity when t 2, lasting 3,
2, 1, seconds
Observe the graph of s as a function of feet to
estimate the instantaneous velocity when t 2.