Review Problems for Mid-Term 1 (MAT1250/Cal Poly Pomona Fall 2018) ( x + 1) 36 [Hint: Find x] x + x x. x 1. = + g.

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1 Prof: M. Nasab Review Problems for Mid-Term (MAT50/Cal Pol Pomona Fall 08). Factor completel 5 +. Find all real zeroes of [Hint: Find ]. Find all real zeroes of ( + ) 6 [Hint: Find ] 4. Add and reduce Rationalize the denominator Graph the following equations: = + b. = + c. = + d. f ( ) = = + f. = + g. = h. f ( ) = ln 7. Find the - and - intercepts of the graph of the equations: = 6 b. + 8 = 8. A manufacturer of DVD plaers has monthl fied costs of $8600 and variable costs of $75 per unit for one particular model. For this model DVD plaer, a) Find the function C ( ) for monthl total costs where denotes the number of units produced and sold. b). Interpret the slope of the cost function and its -intercept in our own words. 9. A small business recaps and sells tires. The business has a revenue function R( ) = 5 and a cost function C( ) = , where represents the number of sets of four tires recapped and sold. b) Find the number of sets of recaps that must be sold to break even. 0. Find the market equilibrium point for the following demand and suppl functions below, where p is price per unit and q is the number of units produced and sold. Demand: p = q + 0, Suppl: p = 6q +. Write the equation of the line passing through the given pair of points (- 6, 5) and (5, 6). [Leave our answer in = m + b form]. Simplif the epression f ( ) f () given the function f ( ) = 4.. Find the slope of the tangent line to the graph of the function below at the given point. f ( ) = 0, (, 4)

2 4. Find the following its: (Using the rules of the derivatives) + b. + c. + ( ) d. t + t t t 5. Suppose that f ( ) = 8 and g( ) c c =. Find the following it: [ f ( ) + g( ) ] c 6. Let f ( ) = + 4,, = Determine the following its. [Hint: Use the graph of the function.]. a) f ( ) b) 0 f ( ) 7. Find the derivative of the following function using the iting process. [Definition of the derivative] f ( ) 9 = b. f ( ) = 0 4 c. f ( ) = + 6 d. f ( ) = f ( ) = f. f ( ) = 6 8. Solve the following equations: a) e = 4 b) ln = 5 9. Draw the tangent lines at the given points (Dots) on the graph. 0. Find the accumulated amount (A) in an account with a principal of $5000 and the interest rate of.5% compounded quarterl for the net 0 ears. [Hint: use r. ( ) n t n A = P + and n = 4]. With an annual rate of inflation of 0% over the net 0 ears, the approimate cost C of goods or services during an ear in the decade is given b C( ) = P(.0) t, with 0 t 0 where t is the time (in ears) and P is the present cost. The price of an oil change for a car is presentl $4.95. Estimate the price 0 ears from now.

3 . Using the rules of the differentiation, find the derivative of the following functions and simplif our answers. f ( ) = + 9 b. f ( ) ( 5) f ( ) 8 = + c. 5 = d. f ( ) = 7 f ( ) = f. f ( ) = ( + 7) g. f ( ) = Application problems for the derivative of a function: Find the marginal cost [ C ( ) ] for b. Find the marginal revenue [ R ( ) ] for C( ) = + 4, 000 at = 0 units. R( ) = c. The demand and cost functions for a product can be modeled b p = 0.00 and C( ) = 0 +, 500, 000 where is the number of units produced.. Write the profit function P(). [Hint: R() =. p, and P() = R() C()]. Find the marginal profit [ P ( ) ]when 0,000 units are produced. Interpret our answer(s). 4. The revenue R in dollars from renting apartments can be modeled b R ( ) = (900 + ). Find the additional revenue (Average revenue) when the number of rentals is increased from 4 to 5.. Find the marginal revenue (The instantaneous revenue) when = 4.. Compare the results of parts (a) and (b). 5. Find the effective rate of interest corresponding to a nominal rate of 7.5% per ear compounded a) Annuall b) Semiannuall c) Monthl

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