studying for a midterm! Please show all the small steps. thank you in advance

velocity at time t. Suppose the position of an object moving in a straight line is given by the specified function. Find the instantaneous 37) s(1) = 12+ 61 + 4,1=4 37) A) 44 B) 32 C) 14 D) 12 Find f'(x) at the given value of x. 38) ((x) = 10x2 + 6x; Find !(8). A) 187 B) -192 C) 208 D) 166 Solve the problem. 39) Suppose that the total profit in hundreds of dollars from selling x items is given by 390 P(x) = -x2 + 8x - 13. Find the marginal profit at x = 6. A) -$100 per item B) -5400 per item C) -5200 per item D) -51200 per item Find the instantaneous rate of change for the function at the given value. 40) f(x) = 5x +9 atx =2 401 A) 10 B) 0 D) 9 Find the equation of the tangent line to the curve when x has the given value. 41) f(x) = 4 *+ 1X=4 A)y = 74X + 75 36 B) y = - 75% * 25 Cy= -* +75 36 Dj y = = 4 25 Solve the problem. 42) The revenue generated by the sale of x bicycles is given by R(x) = 30.00x - x2/200. Find the 42) marginal revenue when x = 1100 units. A) $41.00 B) $ 19.00 C) $30.00 D) 536.67 Find the derivative. 43) f(x) = 2x4 - 8x3 - 4, find f(x) 43) A) 4x3 + 3x2 - 7 B) 8x3 - 24x2 - 7 C) 4x3 + 3x2 D) 8x3 - 24x2 44) g(x) = 4x5 + x4 - 6x2 +2, find g'(-3) 44) A) 1548 B) 1656 C) 1512 D) -72 Find the derivative of the given function. 45) y = (x2 + 2) 45) A) 3x5+ 24x3+ 24x B) 6x5+ 20x3+ 24x C) 6x5 + 24x3+ 24x D) 6x5 + 12x3 + 12x Find the slope of the line tangent to the graph of the function at the given value of x. 46) y = 4x3/2 - 5x1/2, x = 16 46) A) 101 91 192 D) 187 8 Solve the following 47) Find all points of the graph of ((x) = 2x2 + 8x whose tangent lines are parallel to the line y - 44x = 0. 47) A) (10, 280) B) (11, 330) C) (9, 234) D) (13, 442) Solve the problem. 48) The total cost to produce x handcrafted wagons is C(x) = 60 + 5x - x2 + 8x3. Find the marginal cost when x = 4. A) 441 B) 576 9 516 D) 381 Find all values of x (if any) where the tangent line to the graph of the function is horizontal. 49) y = x2 + 2x - 3 49) 9-1 D) 1