Classwork V Sections 3.1, 3.2 Prove that there is no line through the point (1 , 5) that is tangent to y = 4 x 2 . (Leithold 2.1.49). Compute the following using the deﬁnition of the derivative: • d d x (2 x-1) = • d d x ( x 3 ) = • D x ( x 2-x ) = • f0 (2) where f ( x ) = 2 x-1 . • d g d x where g ( x ) = √ 3 x . (3.2.19). Suppose that the revenue R ( n ) in dollars from producing n computers is given by R ( n ) = . 4 n-. 001 n 2 . Find the instantaneous rates of change of revenue when n = 10 and n = 100. (The instantaneous rate of change of revenue with respect to the amount of product pro-duced is called the marginal revenue .) (3.1.20). Suppose a vendor selling turnips at a street fair oﬀers a discount for quantity, so that the average cost per turnip when buying n < 30 turnips is C ( n ) = 4-. 1 n . Find the marginal cost (the instantaneous rate of change of cost – note change of cost not change of average cost) when n = 10 turnips.
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