# Calc Midterm 2

 cost function is the sum of what? fixed costs + variable costs revenue function is the product of what? x(p(x)) profit function is the subtraction of what? r(x)-C(x) marginal =? derivative of function marginal cost is? C'(x) marginal revenue is? R'(x) Marginal profit is? P'(x) elasticity of demand =? -p(f'p)) / f(p) Elasticity of Demand Ex.: p= -.02x+400 1. find x -> f(p)=-50p+200002. find f'(p) -> -503. input values in elasticity -> (-p)(-50) / -50p+20000 for E(p) = 50p / -50p+20000 calculate 100 & explain what it means 1. 50(100) / -50(100)+20000 =.333332. Means when price is \$100 a 1% increase in price will cause .33% decrease in sales When is demand elastic? if E(p) > 1 When is demand unitary? if E(p) = 1 When is demand inelastic? if E(p) < 1 what happens to revenue if E(p) > 1 revenue is decreasing as prince increases what happens to revenue if E(p) <1 revenue increases what happens to revenue if E(p) =1 no change how do you determine the domain of a function? logically figure the numbers that will not =0 how do you find critical numbers of a function? take derivative & set it equal to zero 2nd derivative test take the 2nd derivative of function & set it equal to zero to get relative max & min, then plug max, min & domain into original function what does: f'(c) = 0 & f''(c)>0 indicate in relative extrema? f(c) is relative minimum what does: f'(c) =0 & f''(c) <0 indicate in relative extrema? f(c) is relative maximum what does: f'(c) = 0 & f''(c) = 0 indicate in relative extrema? inconclusive, use first derivative test extreme value theorem: if a function f is continuous on a closed interval [a,b] then f has both an absolute max & min value on [a,b] what value does maximum/minimum refer to? y value how do you make first derivative sign chart? 1. find critical # by solving for DNE or 02. have intervals before & after critical #3. pick number in interval & plug into original function, indicate whether + or - which = increasing or decreasing how do you make second derivative sign chart? 1. find critical # by solving for DNe or 02. have intervals before & after critical #3. pick # in interval & plug into 2nd derivative, indicate whether + or - which = happy or sad face. what is an inflection point? where concavity changes, in sign chart when 2nd derivative = 0 what does the inflection point mean in terms of revenue? tells when the return on money is the greatest how do you find absolute extrema on open interval w/ 1 critical #? 1. find the critical # in (a,b)2. Use 2nd derivative to see if the ritical # gives a relative max or min -> f''(c) >0 = abs min & f''(c) <0 = abs max what are the steps to solving geometric optimization? 1. draw pic2. assign variables3. equation to relate variables4. function in 1 variable & interval weekly demand for photocopying machine is: p=2000-.04x on (0(2000-.04x)x ->2000x-.04x^2P(x)= R(x)-C(x) -> 2000x-.04x^2-(.000002x^3-.02x^2+1000x+120000) -> -.000002x^3-.02x^2+1000x-120000 2. find the marginal revenue function & marginal profit function marginal revenue: R'(x) =200-.08xmarginal profit P'(x)=.000006x^2-.04x+1000 3. what is the total profit for 5000 copiers? what is the profit from the 5000th copier? P(5000) = \$4,130,00P(5000) -P(4999) = \$650.05 how do you find the price of the 100th, 200th, 300th, etc. item? P(x) for the 100th - P(x) for the 99th Authorjazzybeatle ID67651 Card SetCalc Midterm 2 Descriptionstuff Updated2011-02-21T18:43:28Z Show Answers