Solved Problems for Derivatives: Graphing functions

Here we will show some typical problems related to sketching graphs of functions.
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Note that problems that ask for sketching a graph also include all other types listed on the list of problems below (domain and limits, asymptotes, monotonicity, concavity).

Problem: Find the domain and limits at endpoints of its intervals for the function
Problem: Find the domain and limits at endpoints of its intervals for the function
Problem: Find the domain and limits at endpoints of its intervals for the function
Problem: Determine all asymptotes of
Problem: Determine all asymptotes of
Problem: Determine maximal intervals of monotonicity and local extrema for
Problem: Determine maximal intervals of monotonicity and local extrema for
Problem: Determine concavity of the function
Problem: Sketch the graph of the function

f (x) = 3x⁴ − 8x³ + 6x².
Problem: Sketch the graph of the function
Problem: Sketch the graph of the function
Problem: Sketch the graph of the function
Problem: Sketch the graph of the function
Problem: Sketch the graph of the function