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