Ma 113 Functions And Inverse Functions, The Exponential Function And The Logarithm Worksheet Page 22
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4110. The sides of a rectangle are varying in such a way that the area is constant. At a certain instant the
length of a rectangle is 16 m, the width is 12 m and the width is increasing at 3 m/s. What is the rate
of change of the length at this instant?
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11. Suppose f and g are differentiable functions such that f (2) = 3, f (2) =
1, g(2) =
, and g (2) = 2.
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Find:
2
(a) h (2) where h(x) = ln([f (x)]
);
3
(b) l (2) where l(x) = f (x
g(x)).
12. Abby is driving north along Ash Road. Boris driving west on Birch Road. At 11:57 am, Boris is 5 km
east of Oakville and traveling west at a speed of 60 km/h and Abby is 10 km north of Oakville and
traveling north at a speed of 50 km/h.
(a) Make a sketch showing the location and direction of travel for Abby and Boris.
(b) Find the rate of change of the distance between Abby and Boris at 11:57 AM.
(c) At 11:57 AM, is the distance between Abby and Boris increasing, decreasing, or not changing?
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