Framing an Appropriate Research Question 6b9b26d93da94caf993c038d9efcdedb.pdf
Domain, Limits, Continuity, Derivatives, Critical Points, Inflection, Asymptotes and Graph of a Piecewise Function
1. Exercise.
We dene
f(x) =
3 p
x
3 p
jxj + 1
:
(1) Find the domain of f.
(2) Compute limx!1 f(x) and limx!1 f(x).
(3) Is f continuous in its domain? Explain why.
(4) Compute f0(x). (If f0(x) does not exist, explain why.)
(5) Compute f00(x). (If f00(x) does not exist, explain why.)
(6) Find all critical numbers.
(7) Find all points of inection.
(8) Find all asymptotes.
(9) Draw the graph of f.
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