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Unformatted text preview: day before. (B) After 2 days on the job, the new employee can assemble 3.7 bikes/day. (C) After 2 days on the job, the new employee needs to learn to assemble 3.7 more bikes/day. (D) None of these. 13. Let f (x) = √ x + 2 and g (x) = 18x2 − 11. Find f (g (x)). (A) f (g (x)) = 18x + 25
(D) f (g (x)) =
18x2 − 9 √
(B) f (g (x)) = 3x 2 + 3 √
(C) f (g (x)) = (18x2 − 11) x + 2 (E) None of these 14. Write the function y = (9 − x2 )1/3 as a composition of two functions. 15. Find the derivative of the function f (x) = 47(9x3 − 8)3/2 . 16. Find the derivative of the function f (x) = (5x + 1)5 (4x + 1)−2 . 17. Consider the following table of values of the functions f and g and their derivatives at various points.
x 2 3 4 f ( x) 3 4 1 2 f ( x) 4 6 9 8 g ( x) 3 4 2 1 g ( x)
Find 1 5/9 4/9 8/9 1 d
[g (f (x))] at x = 3.
dx
(A) less than 6 (B) between 6 and 2 (D) between 2 and 6 (E) more than 6 (C) between 2 and 2 18. Find the equation of the tangent line to the graph of
f (x) = x2 + 24
at x = 5. (A) y = 5
(x − 5) + 7
7 (B) y = 5
(x − 7) + 5
7 (D) y = 1
(x − 7) + 5
14 (E) None of these (C) y = 1
(x − 5) + 7
14 19. Suppose the demand for a certain brand of a product is given by
D ( p) = − p2
+ 450.
104 where p is the price in dollars. If the price, in terms of the cost c, is expressed as p(c) = 2c − 12, ﬁnd
the demand function in terms of the cost. 20. Find the derivative of the function f (x) = −4e−2x . 21. Find the derivative of the function g (x) = 2e4x+1 . 22. Find the derivative of the function h(x) = (2x2 − 4x + 4)e−4x . 23. Find the derivative of the function f (x) = 8e4x
.
5x − 2 24. Find the derivative of the function g (x) = 46x+1 . 25. Find the equation of the tangent line to f (x) = e2x + 3 at x = 0. 26. The sales of a new hightech item are given by
S (t) = 9400 − 9000e−0.4t ,
where t represents time in years. Find the rate of change of sales after 5 years. (Round to one decimal
place as needed.)
(A) 3.3 (B) 487.2 (C) 8182.0 (D) 9887.2 (E) None of these 27. Using data in a car magazine, we constructed the mathematical model
y = 100e−0.08044t
for the percent of cars of a certain type still on the road after t years. Answer parts (i) and (ii)
(i) Find the percent of cars on the road after 5 years.
The percent of cars is
(A) less than 50% (B) between 50% and 60% (D) between 70% and 80% (C) between 60% and 70% (E) more than 80% (ii) Find the rate of change of the percent of cars still on the road after 5 years.
The rate of change is
(A) less than 10% per year (B) between 10% and 7% per year (C) between 7% and 4% per year (D) between 4% and 1% per year (E) more than 1%...
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This note was uploaded on 01/14/2014 for the course MATH 116 taught by Professor Jess during the Fall '09 term at University of Arizona Tucson.
 Fall '09
 JESS
 Calculus, Derivative

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