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Unformatted text preview: Math 184 Midterm Review Questions 1. Use limits to find the derivative of the function f ( x ) = x 2 + 3. 2. If the function f ( x ) = braceleftBigg ax 2 + ax- 1 if x <- 1 x 3 if x ≥ - 1 is differentiable at x =- 1, then what is the value of a ? 3. Suppose that the cost for producing x units of some product, measured in thousands of dollars, is given by C ( x ) = 300 200 − √ x . Compute the cost C (10000) of producing 10000 units. Compute the marginal cost C ′ (10000) of producing 10000 units. Use this to approximate the cost of producing 9998 units. 4. Find the derivatives of the following functions. a. f ( x ) = ( x 2- 1) 4 ( x 2 + 1) 5 b. g ( x ) = e e + e x + x e c. h ( x ) = ( x 2 + 1)( x 3 + 1)( x 4 + 1) d. q ( t ) = tan( √ t ) (remember that tan x = sin x cos x ) 5. A ball thrown upwards from the top of a building 100 feet tall has height of h ( t ) = 100 + 60 t- 16 t 2 above the ground after t seconds....
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This note was uploaded on 11/03/2009 for the course ECON 210 taught by Professor James during the Spring '09 term at The University of British Columbia.
- Spring '09