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Practice Midterm 1

# Practice Midterm 1 - 3 Find the derivative of f x = 2...

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Name: _________________________________________ Section (assigned): ______ Section (attended): _______ Math 10A Practice Midterm 1 February 1, 2008 Notes allowed (one page), graphing calculators allowed, show all work 50 points total, each problem worth 10 points 1. If possible, choose a constant k so that the following function is: a. Continuous on any interval: h x ( ) = x 3 " 3 x 2 + 2 x x " 2 x # 2 k + 1 x = 2 \$ % b. Differentiable at x = 0 : g x ( ) = x x < 0 x 2 + kx x " 0 # \$ % % 2. We are given a position function of an object as s ( t ) = 2 t . a. Find the average velocity of the object on the intervals [2, 2.1], [2, 2.01], and [2,2.001]. t 2 2.001 2.01 2.1 f t ( ) 4 4.00277355 4.0278222 4.28709385 b. Estimate the instantaneous velocity at t = 2 using your answer in part (a).

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Unformatted text preview: 3. Find the derivative of f x ( ) = 2 x " 2 at the point x = " 2 using the definition " f a ( ) = lim h # f a + h ( ) \$ f a ( ) h . Find the equation of the tangent line at the point x = " 2 . 4. Given the function f x ( ) = " 2 x 2 : a. Estimate " f x ( ) by using the average rate of change formula. Let h = 0.1. b. Calculate " f x ( ) using the definition " f x ( ) = lim h # f x + h ( ) \$ f x ( ) h . 5. The graph of f is given below. At which of the marked x-values can the following statements be true? No justification is necessary . a. f x ( ) < b. " f x ( ) < c. " " f x ( ) < d. f x ( ) is increasing e. " f x ( ) is increasing...
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Practice Midterm 1 - 3 Find the derivative of f x = 2...

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