If f(x) = 7 sin (x), then f'(x) = Find the slope of the tangent line to the curve -2x+3xy-4y: == -134 at the point (2, 3). Consider a closed rectangular box with a square base with side x and height y. a. Find an equation for the surface area of the rectangular box. S(x, y) b. If the surface area of the rectangular box is 64 square feet, find dy dx when x = = 4 feet and y = 2 feet. dy || 33 dx Let f(t)=5t48t+ 4et. Then f'(t): = If f(x) = 3x ln(x), find f'(x). Find f'(3). y = (7 +6 x) * Use Logarithmic Differentiation to find dy dx dy dx dx dy Find at x = -5 if y = = x+5 and = 2. dt dt dx dt At noon, ship A is 50 nautical miles due west of ship B. Ship A is sailing west at 17 knots and ship B is sailing north at 19 knots. How fast (in knots) is the distance between the ships changing at 5 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.) knots An inverted pyramid is being filled with water at a constant rate of 25 cubic centimeters per second. The pyramid, at the top, has the shape of a square with sides of length 7 cm, and the height is 13 cm. Find the rate at which the water level is rising when the water level is 11 cm. cm/sec h b b Use linear approximation, i.e. the tangent line, to approximate 36.1 as follows: Let f(x)=x. Find the equation of the tangent line to f(x) at x = = 36 L(x) = Using this, we find our approximation for 36.1 is NOTE: For this part, give your answer to at least 9 significant figures or use an expression to give the exact answer. Let y = 3x. Find the change in y, Ay when x = 2 and Ax = 0.4 Find the differential dy when x = 2 and dx = 0.4