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Unformatted text preview: Math 170010 Homework 9/7 Fall 2011 Goal:
• Given tangent slope ﬁnd location by successive numerical approximation.
Note: You MAY NOT use any techniques of diﬀerentiation that you might know from other classes.
Every derivative must be computed by
• Table of secant slopes, followed by guessing a tangent slope.
Warm Up: (If you were in class on 9/6, you already did most or all of this.)
1. For f (t) = tet , compute f ′ (2).
2. Graph f . In your graph, sketch the tangent line at location t = 2.
3. If you were to guess a location where tangent slope is 10, would you look left or right of t = 2?
4. Guess a location where tangent slope is 10. Use your guess as the ﬁxed location and compute
f ′ there. Use the usual table of ﬁxed end, free ends, and secant slopes.
Exercises:
1. For f (x) = 5 ln x, ﬁnd where f ′ (x) = 1.5. Use a technique similar to the warm up. Keep
making new guesses for the location until your tangent slope computation produces 1.50.
2. The height of a falling object is given by
h(t) = 3000 − 35t − 125e−7t/25
where h is measured in feet and t is in seconds. (This is the skydiver from week one homework.
At what instant in time is the object falling at −20 ft/sec?
Challenge Problems: 1 1. The graph at right shows a function,
f (x) = 1
x and the tangent line at location x = 2.
[Warning! Graph is not to scale]
(a) Compute f ′ (2).
(b) Write the equation of the tangent line.
[Hint: Use the slope you just computed,
and the x and y coordinates of the point
of tangency.]
(c) Where does the tangent line cross the y axis
2. The graph at right shows a function,
f (x) = 1
x and the tangent line at an unknown location.
[Warning! Graph is not to scale]
If the tangent line crosses the y axis at 1.5,
where is the point of tangency? Hints and Answers
Warm Up:
1) 22.167. 3) left. 4) 1.419 would be a very good guess.
Exercises:
1) x ≈ 3.333. 2) t ≈ 3.026 sec.
Challenges:
1a) 0.25; 1b) y = 1 − 0.25x; 1c) 1. 2) x ≈ 1.333
2 ...
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 Fall '08
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 Calculus, Approximation, Derivative, Slope, tangent slope

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