On the moon, the acceleration due to gravity is 8 ft/sec. A frozen tofurkey is dropped from the top of a tall vertical tower that is on the moon, and the tower is 200 feet tall. How fast is the frozen turkey travelling at the instant it hits the ground? Find a function f that satisfies the following conditions: (1) f(0) = 1 (11) f'(2) =13 (III) f"(x) = 6x-2 Given constants a and b, Find and classify all critical values for f (x) = ax+-, a #0 &b #0Show that y = A + Ce" is a solution to " = k(y - A). dt a. Use implicit differentiation to find "Y for x2 + 2x - 2y + y2 = 47. b. Use from part a. to find all possible slopes for the tangent line(s) when y = 1.a. Find the equation of the tangent line to f (x) = x2 at the point (9,81). b. Use the tangent line equation to approximate (9.01)2. Compare your result with the value from a calculator (the actual value). c. Which value is larger, the tangent line estimate or the actual value? Why? Find the dimensions of a cylinder with minimum surface area and volume 1 liter.00 A rectangular storage container with an open top is to have a volume of 1. The length of its base is twice the width. Material for the base costs $10 per square meter. Material for the sides costs $6 per square meter. Find the cost of materials for the cheapest such container. Find the point on the curve 2x + 3y = 7 that is closest to the origin.10 If a and b are the legs of a right triangle with hypotenuse 1, find the largest possible value of 2a + b. 11 A bug moves along the xy-plane, with motion described by the equations x = t3 - 3t and y = 2t3 - 9t2 + 12t a. Does the bug ever come to a complete stop? If so, when? b. Does the bug ever move straight up or down? If so, when and where? c. Is the bug ever moving straight horizontally right or left? If so, when and where