Methods of Calculus MAC3233 Test 1 January 31, 1996 Instructions: Do not write your answers on this paper, use separate answer sheets. This is a closed-book test. No calculators are allowed to be used. To receive credit, you must show all work. You are not required to simplify your answers. 1. (10 pts.) If f ( x ) = 1 √ x , compute f (4) and f0 (4). Find the equation of the tangent line to the graph of y = f ( x ) at the point where x = 4. 2. (10 pts.) Find dy dx , if y = x + 1 79 . 3. (10 pts. each) Diﬀerentiate: (a) f ( x ) = 5 x + 8 x-3 (b) f ( x ) = ( 3-2 x + x 5 ) 2 3 (c) f ( x ) = 8 x 2-2 x + 161 4. (10 pts.) Suppose a ﬁrm’s proﬁt from producing and selling x units of a product is given by P ( x ) = 32 x 2-9 x 3 thousands of dollars. Find the marginal proﬁt at a production level of 8. 5. (10 pts.) An object is thrown upward. Suppose s ( t ) = 4 + 100 t-16 t 2 is the height of the object, in feet, after t seconds. (a) Find the velocity function
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