Find the points of inflection for the function: f(x) = x^3 ln(x/3).


Find the points of inflection for the function: {eq}f(x) = x^3 \ln(\frac{x}{3}) {/eq}.

Points of Inflection:

Points of inflection are points on the graph of a function where concavity changes. To determine where concavity changes we first take the second derivative, determine where it equals 0 or does not exist. Then we use these values to create open intervals, from which we choose test values to plug into {eq}f''(x). {/eq} Then if this value is negative, the graph is concave down on that interval, and if it is positive the graph is concave up on that interval.

Answer and Explanation:

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Using the product rule the first derivative is...

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Concavity and Inflection Points on Graphs


Chapter 9 / Lesson 5

You might not think of a cup when you think of an awesome skateboard ramp. But I'm sure a really bad ramp would give you a frown, right? Learn about cups and frowns in this lesson on concavity and inflection points.

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