Considering the following graph of the given function f. y The xy-coordinate plane is given. The curve enters the window in the second quadrant nearly horizontal, goes down and right, crosses the negative x-axis, changes direction on the negative y-axis, goes up and right, crosses the positive x-axis, and exits the window in the first quadrant nearly horizontal. Use the graph of f to complete the following table. f(x) f'(x) x > 0 f(x) > 0 F'(x) ? v0 f(x) < 0 F'(x) ?0 x >0 x < 0 f(x) > 0 f'(x) ? 0 x < 0 f(x) < 0 F'(x) ?v 0 Sketch the graph of f and f' on the same coordinate axes. у

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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.