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Unformatted text preview: Homework 2/12
Identify each problem as:
Type I: Given location, ﬁnd slope, or
Type II: Given slope, ﬁnd location.
Then solve each problem.
1. An object is launched upward from a tower so that after t seconds its height above ground is
h(t) = 100 + 60t − 16t2 feet.
(a) What is its velocity after 1 second?
(b) What is its velocity after 3 seconds?
(c) When is its velocity −60 ft/s?
(d) What is its velocity at the time when it hits the ground?
(e) How high is it when its velocity is −68 ft/s?
2. The graph of f (x) = x3 − x2 (shown at
right) has two tangent lines with slope 1. 1 (a) Find the equations of those lines.
(b) Sketch them in the graph at right. 0.5 –1 –0.5 0.5
0 –0.5 –1 –1.5 –2 1 1 1.5 1
has a tangent line
that passes through (0, 1.5) as shown at
right. 3. The graph of f (x) = 2
1.5 (a) Where is the point of tangency?
1 (b) Find the equation of the tangent line
at the point (2, 0.5). Sketch this line
in the graph at right. 0.5
–0.5 1 2
x –1 Hints and Answers
1. a) (I) 28 ft/s; b) (I) −36 ft/s; c) (II) 3.75 s; d) (I) −100 ft/s; e) (II) 84 ft.
2. Hint: One of the locations is x = −1/3.
3. a) (II) x = 4/3; b) (I) y = −x/4 + 1. 2 3 4 ...
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