Problem 1 Find the indefinite integral a. J ( 2 + 3 -5) dx b. J 6x x2 + 3 dx Problem 2 Evaluate the definite integral. Round to the fourth as needed. a. Jo xe 5x7+7dx b. So ( Vx + x3) dx Problem 3 A well company finds that their marginal profit, in dollars per foot, from drilling a well that is x feet deep is given by P' (x) = 20Vx. Find the total profit when a well that is 250 feet is drilled. Round to the second as needed. Problem 4 Find f' (x) for f(x) = -+3x3 - x4. Problem 5 Graph the function f(x) = x2 - 6x + 5 by finding the vertex, x intercepts and y intercepts. Find equation of the tangent line at x = 2 and graph it. Problem 6 Find the First and Second Derivative f(x) = (3x2 + 4)3 Problem 7 Find the coordinates of critical values, classify the critical values as relative min, max or neither; b. identify intervals where the function is increasing or decreasing; c. find coordinates of any inflection points; d. identify intervals where the function is concave up or down; e. sketch the function labeling all relevant coordinates. f(x) = x3+6x2 -15x -20 Problem 8 Suppose a manufacturer is selling a new product. The revenue and cost are determined by: x = number of units R(x) = -x2+ 24x C(x) = 12x + 28 a. What number of units will maximize profit? b. Find the cost, revenue and profit for that number of units that maximize profit