## Test 3

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## Test 3

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- Pages:
- 4
- School:
- Arizona State University
- Course:
- Mat 210 - Brief Calculus

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MAT 210 Test 3 Page 2 1 Let f x x 3 12 x 1 a 4 pts Find all the critical values of f algebraically b 4 pts Use the first derivative to find the largest open interval s on which f x is increasing Show your work c 4 pts Find the largest open interval s on which f x is decreasing d 2 pts Find all relative maxima e 2 pts Find all relative minima f 4 pts Find all absolute maxima and absolute minima of f x restricted to the interval 5 3 S01A Copyright 2001 Arizona State University MAT 210 Test 3 Page 3 2 Let f x 5 8 x 3 2 x 4 a 4 pts Find f b 4 pts Use the second derivative to find the largest open interval s on which f x is concave up Show your work c 4 pts Find the largest open interval s on which f x is concave down d 4 pts Find the point s of inflection 3 a 4 pts Given the equation x 2 y 2 x y 3 1 find dy dx b 4 pts Use your answer to part a to find the slope of the tangent to the curve x 2 y 2 x y 3 1 at the point 2 1 c 4 pts Use your answer to part b to find the equation of the tangent to the curve x 2 y 2 x y 3 1 at the point 2 1 4 6 pts each Find the following indefinite integrals S01A Copyright 2001 Arizona State University MAT 210 Test 3 a 3 ln x 4 x dx b 5 xe c 2x3 x 4 4 dx x2 2 Page 4 dx 1 5 10 pts Evaluate 3t 2 4t 3 8 dt using the Fundamental Theorem of Calculus 0 Show your work 6 8 pts A bus company charges 60 per person for a sight seeing trip and obtained 40 people for the trip The company has data that indicates that for the same trip each 2 increase in the S01A Copyright 2001 Arizona State University MAT 210 Test 3 Page 5 price above 60 results in the loss of one customer What should the company charge to maximize revenue 7 8 pts Find the cost function C x for an adhesive tape manufacturer if the marginal cost C x in dollars per tape is given by C x 150 0 01e x where x is the number of tapes produced and fixed costs are 100 8 8 pts Suppose copper is being extracted from a certain mine at the rate given by P t 100e 0 2 t where P t is measured in tons of copper and t in years At this rate how much copper will be extracted during the third year Sketch the graph of P t and shade the region between the graph and the x axis that represents the amount of copper extracted in the third year S01A Copyright 2001 Arizona State University

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