short2a

short2a - 2 ft/s how fast is he walking 15 6 6(10 pts A...

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Exam 2, Form A M170-007 Fall, 2010 Name: (1 pt.) Show all your work. 1. (10 pts.) For each function below, compute f ( x ). I don’t expect you to show much, if any, work. Assume that c is a constant. (a) f ( x ) = sin x (b) f ( x ) = cos x (c) f ( x ) = e x (d) f ( x ) = x c (e) f ( x ) = ln x 2. (20 pts.) For each function below, compute f ( x ). Assume that g is an unknown function of x and a , b and c are constants. (a) f ( x ) = e kx sin( ax + b ). (b) f ( x ) = ax 3 bx 2 + cx (c) f ( x ) = x 2 tan x (d) f ( x ) = p 2 g x + x P 3 3. (15 pts.) The graph of the curve y 3 + yx 2 + x 2 - 3 y 2 = 0 is shown below. Find the equation of the tangent line to the curve at the point ( - 1 , 1). Then graph the tangent line on the same axes as the curve. 1

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4. (15 pts.) The graph of g ( x ) = x - 1 + sin(2 x ) is shown at right. It has two horizontal tangents in the domain [0 , π ]. Find their locations. Be sure to show all your work. 2
5. (15 pts.) A 6 foot tall man is walking uphill away from a 15 foot tall light pole. (As depicted, hope- fully, at right.) If the length of his shadow is changing at 1
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Unformatted text preview: . 2 ft/s, how fast is he walking? 15 6 6. (10 pts.) A population of rabbits and a population foxes share a common habitat. The number of foxes as a function of time is F and the number of rabbits as a function of time if R . Observations indicate that the quantity 900( F-20) 2 + ( R-400) 2 is always constant. Suppose that at some point in time there are 250 rabbits and 15 foxes, and that at this time the rabbit population is increasing at a rate of 60 rabbits per year. What is the rate of change of the fox population at this time? 7. The graphs of a function, f , and its derivative, f ′ , are shown at right. Suppose that g ( x ) = x 2 f ( x ) (a) (5 pts.) Find g ′ ( x ). (b) (5 pts.) Estimate g ′ (2). (It is your job to deduce which graph is f and which is f ′ .) (c) (5 pts.) Estimate g ′′ (2). 3...
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short2a - 2 ft/s how fast is he walking 15 6 6(10 pts A...

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