For the function f (x) = x^3 / (x^2 - 4) defined on the interval [-20, 20], find the region where...


For the function {eq}\displaystyle f (x) = \frac{x^3}{x^2 - 4} {/eq} defined on the interval {eq}[-20,\ 20] {/eq}, find the region where the function is concave up.

Concavity of Function:

Given a function {eq}f(x) {/eq} inflection points arise when first order derivative {eq}f''(x)=0 {/eq}.

Morever, the function is concave upwards when {eq}f''(x) >0 {/eq} and concave downwards when {eq}f''(x) <0 {/eq}

Answer and Explanation:

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Given the function

{eq}\displaystyle f (x) = \frac{x^3}{x^2 - 4} {/eq} defined on the interval {eq}[-2,\ 2] {/eq}

its second derivative is...

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Learn more about this topic:

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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