MAT 210 Test #3MAT 210 Test #31. Let xxxxf 223)(23(a) [4 pts] Find all critical values algebraically.(b) [2 pts] Find the largest open interval(s) on which f(x) is decreasing.(c) [2 pts] Find all relative maxima.(d) [2 pts] Find all relative minima.(e) [4 pts] Find the inflection value(s) algebraically.(f) [2 pts] Find the largest open interval(s) on which f(x) is concave down.(g) [4 pts] Find the location of all absolute maxima and absolute minima of f(x) restricted to theinterval [-3, 4]2.(a) [4 pts] Given the equation ,922 yx find dxdy.(b) [2 pts] Use your answer to part (a) to find the slope of the tangent to the curve ,922 yxat the point )5 ,2(.(c) [4 pts] Use your answer to part (b) to find the equation of the tangent to the curve,922 yx at the point )5 ,2(.3. [5 pts each] Find the following indefinite integrals:(a)dxxx3)(ln(b)dxxex325(c)dxxx 4434. [5 pts] Find dxx50225 by finding the area of the appropriate geometric region. SketchMAT 210 Test 3 Page 2the geometric area.5. [8 pts] Evaluate 1032)843( dttt using the Fundamental Theorem of Calculus.6. Suppose that the concentration C(t) of a drug in the blood stream t hours after it was taken orally is given by 0 ,2)5.()(  ttetC.(a) [5 pts] Use a graphing utility to find the hour at which the concentration of the drug in the blood stream is at an absolute maximum. Sketch the graph, and label the approximate position of the absolute maximum.(b) [5 pts] An inflection point occurs after the concentration has reached a maximum and beginsto decrease. Use a graphing utility to find the hour at which this inflection point occurs?7. [10 pts] Find the cost function C(x), if the marginal cost )(' xC, in dollars per item , is given by 10033.0)('2 xxxC, where x is the number of items produced and fixed costsare $1000.8. [10 pts] After the introduction of a new camera, the rate of sales in thousands per month is given by 2/1)31(5)(' ttN, where t is in months. Find the number sold in the first 6 months. Sketch the graph of )(' tNand shade the region between the graph and the x-axis that represents the number of cameras sold in the first six months.9.(a) [6 pts] Algebraically, find the points of intersection of the two curves 1 and 12 xyxy. (b) [6 pts] Find the area enclosed by the two curves given in part (a). Sketch the curves, shade the region between the two curves, and write the integral that represents the area between the two curves.F00A Copyright 2000 Arizona State