An object moves along the y-axis (marked in feet) so that its position at time x (in seconds) is given by the function f(x) = x° - 12x2 + 36x. a. Find the instantaneous velocity function v=f'(x). b. Find the velocity when x= 1. c. Find the time(s) when v = 0. a. v= b. The velocity of the object at x = 1 is ft/s. (Simplify your answer.) c. The velocity is zero at x= seconds. (Simplify your answer. Use a comma to separate answers as needed.)

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.