III. Consider the function f(x)=x(x-3)² a) Establish the domain of the function, and write it in interval notation b) Determine the intersections with the coordinate axes c) Determine if the function is even, odd or neither of them d) Determine the vertical, horizontal or oblique asymptotes of the function. Set appropriate limits e) Use the first derivative to determine the intervals of increase, decrease, maximum points and minimum points f) Use the second derivative to determine the intervals of concavity down, concavity up and the inflection points
III. Consider the function f(x)=x(x-3)² a) Establish the domain of the function, and write it in interval notation b) Determine the intersections with the coordinate axes c) Determine if the function is even, odd or neither of them d) Determine the vertical, horizontal or oblique asymptotes of the function. Set appropriate limits e) Use the first derivative to determine the intervals of increase, decrease, maximum points and minimum points f) Use the second derivative to determine the intervals of concavity down, concavity up and the inflection points
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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III. Consider the function f(x)= x(x-3)²
a) Establish the domain of the function, and write it in interval notation b) Determine the intersections with the coordinate
axes
c) Determine if the function is even, odd or neither of them
d) Determine the vertical, horizontal or oblique asymptotes of the function. Set appropriate limits
e) Use the first derivative to determine the intervals of increase, decrease, maximum points and minimum points
f) Use the second derivative to determine the intervals of concavity down, concavity up and the inflection points
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