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Test 3 sample_1 - Sample Test This test will cover 4.4-5.6...

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Sample Test This test will cover 4.4-5.6, excepting 4.6 (Related Rates, which we skipped) This is probably longer than the actual test will be. Part I 1. Find y' for y = e x 2 2. Find dy dx for x 2 y 2 = 25 3. f x = ln 3x 1 Find f '( x ) 4. x 2 y 2 e xy = 20 Find y ' 5. The graph of the equation 9 x 2 4 y 2 = 36 is an ellipse. Find the points ( x and y coordinates) where this ellipse has horizontal and vertical tangent lines. (There will be two of each.) Part II For the following problems, determine where the function is increasing, where it is decreasing, where it is concave up, and where it is concave down. (Express answers in interval form.) Find any local maxima or minima, and any points of inflection. 6. f x = x 4 x 5 3 (Note: finding concavity/points of inflection may require use of the quadratic formula. You may either give the exact solution, with radicals, or an approximate solution, rounded to two decimal places.) 7. f x = ln x 2 10 8. Sketch a graph that satisfies the following table.
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