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mt165f2009_2

# mt165f2009_2 - 4(10 points Consider the function f x = 2 3...

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Math 165 Midterm Exam Second Part Name & Section: Instructor: Answer each question completely. Show all work. No credit is allowed for mere answers with no work shown. Show the steps of calculations. State the reasons that justify conclusions. 1. (10 points) Consider y = f ( x ) = x 2 + 8. (a) Find the equation of the tangent line to the graph of f ( x ) at the point where x = 1. (b) Tell where this tangent line intersects the x -axis.

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2. (10 points) A child is flying a kite. The kite is 60 feet above the child’s hand and blowing on a horizontal course. When 100 feet of string are out, the string is playing out at 5 feet per second. At that instant, how fast is the kite moving? Be sure to include the units in your answer.
3. (10 points) Consider f ( x ) = 2 x 3 - 3 x 2 - 36 x + 1. (a) Find the critical points of f ( x ) on [0 , 5] . (b) Find the maximum value of f ( x ) on the interval [0 , 5] and where it occurs. (c) Find the minimum value of f ( x ) on the interval [0 , 5] and where it occurs.

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4. (10 points) Consider the function
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Unformatted text preview: 4. (10 points) Consider the function f ( x ) = 2 3 x 3-5 x 2 + 12 x . (a) Find all intervals where f is increasing. (b) Find all intervals where f is decreasing. (c) Find all intervals where f is concave up. (d) Find all intervals where f is concave down. (e) Find all inﬂection points of f ( x ). 5. (10 points) Suppose that f ( x ) is a twice-diﬀerentiable function and that the graph of y = f ( x ) is shown below. L M 3, M 1 R L 2, M 1 R y E f L x R (a) Which of the following best describes the value of f (0)? A. It is positive. B. It is negative. C. It is zero. D. Its sign cannot be determined from the graph. (b) Which of the following best describes the value of f 00 (-3)? A. It is positive. B. It is negative. C. It is zero. D. Its sign cannot be determined from the graph. (c) How many inﬂection points does f have in the interval [-3 , 2]?...
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