MAT 210 Test 3 Page 1. Let 112)(3 xxxfa) [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 University2MAT 210 Test 3 Page 2. Let 43285)( xxxf .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 inflection3.a) [4 pts] Given the equation ,1232 yxyx find dxdy.b) [4 pts] Use your answer to part (a) to find the slope of the tangent to the curve1232 yxyx at the point )1 ,2(.c) [4 pts] Use your answer to part (b) to find the equation of the tangent to the curve,1232 yxyx at the point )1 ,2(.4. [6 pts each] Find the following indefinite integrals:S01A Copyright 2001 Arizona State University3MAT 210 Test 3 Page a)dxxx4)(ln3b)dxxex 225c)dxxx )4(2435. [10 pts] Evaluate 1032)843( dttt using the Fundamental Theorem of Calculus.(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 theS01A Copyright 2001 Arizona State University4MAT 210 Test 3 Page 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,)(' xC, in dollars per tape, is given by xexC 01.0150)(' , 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 bytetP2.0100)(', 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 )(' tPand 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