Differential Calculus Exercise Problem #1 Let f be a function satisfying the following properties: Continuous on R \ {0} f(-1) = -4 f0) = 1 and f (플)=: lim f(x) = 0 x-+00 lim [f(x) – (x – 2)] = 0 x--00 lim f(x) = 1 x-0+ lim f(x) = -∞ x-0 Moreover, the table of signs for f' and f" is given below. (-0, –1) -1 (-1,0) 2 0.58 V3 +00 f'(x) f"(x) иnd иnd + 1. Give equations of the three linear asymptotes of the graph of f. 2. Determine where is f increasing or decreasing and concave up and concave down. Determine the relative maximum, relative minimum, and inflection points of the graph of f (if any). 3. Sketch the graph of f with emphasis on concavity. Label all the relative extremum points, and inflection points with their respective coordinates, and the asymptotes with their respective eguations

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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.