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Final Review 2

# Final Review 2 - 5 Suppose the price and demand of a...

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MATH 1331 Spring 2006 Final Exam Review #2 Rules for Derivatives d dx ( c ) = 0 d dx ( x n ) = nx n - 1 d dx ( e x ) = e x d dx (ln x ) = 1 x d dx ( f ( x ) · g ( x )) = f ( x ) · g ( x ) + g ( x ) · f ( x ) d dx f ( x ) g ( x ) = f ( x ) · g ( x ) - g ( x ) · f ( x ) [ g ( x )] 2 d dx ( f ( g ( x ))) = f ( g ( x )) · g ( x ) CHAPTER 3 and 4: Derivatives and Elasticity 1. Find the instantaneous rate of change of R ( x ) = 10 x - . 001 x 2 when x = 5 and interpret. 2. Suppose the demand equation is given by p ( x ) = 1000 x + x 2 . Find the instantaneous rate of change of price with respect to the number sold.

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3. Given that the cost equation is C ( x ) = 165 x - . 5 and the revenue was \$64 per item, find (a) marginal cost. (b) marginal revenue. (c) marginal profit. 4. Find the derivative of the following functions. (a) x 4 ln x (b) x 3 - 1 x 2 + 2 (c) 100 1 + e - x (d) 3 ( x + 1) 4 (e) (2 x - 3) 5 (4 x + 7) (f) xe - . 02 x (g) ln(5
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Unformatted text preview: 5. Suppose the price and demand of a commodity is related by p ( x ) = e-2 x . (a) Find the marginal revenue. (b) Find where marginal revenue is zero. (c) Where is marginal revenue positive? 6. The eﬀect of prices on pens was studied. It was estimated that the demand equation was x = 10 p-29 , where x is the number of pens purchased, and p is the price in dollars. (a) Find the elasticity of demand when p = 1. (b) Classify the demand as inelastic, unit elastic or elastic. (c) Find the (approximate) price of a pen that gives unit elasticity....
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Final Review 2 - 5 Suppose the price and demand of a...

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