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UFCalcSet12

# UFCalcSet12 - Exercises UF Calculus Set 12 1 Use the graph...

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Exercises UF Calculus Set 12 1. Use the graph of f ( x ) below to estimate, to the nearest multiple of 0.5, the values of f 0 ( x ) at the points x = - 5 , - 2 , 0 , 1 , 4 , 7 . 2. Inspect the graphs below. The first represents the milliliters of a drug in the bloodstream after ingesting medicine as a function of the time elapsed in minutes; the second represents the profit in thousands of dollars a company receives as a function of the selling price in cents. (a) Make a rough sketch of the derivative in each case. (b) State in words what f 0 (10) = 5 would represent in each case, including units. 3. Find the derivative of the given function; state the domain of f and its derivative. (a) f ( x ) = 2 - 5 x (b) f ( y ) = 3 y - 1 + 4 y (c) f ( x ) = 1 3 - 2 x (d) f ( x ) = (1 + x ) 2 (e) f ( x ) = 1 2 x - 3 (f) f ( x ) = x x - 3 4. Find the second derivative of the function (a) y = 1 x (b) y = t 3 - 4 t 2

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5. In the curve y = f ( x ) illustrated below, identify the points x = c where each of the following happens: (a) f is discontinuous at x = c .
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