Question
Asked Oct 18, 2019
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Determine where the graph of the function is concave upward and where it is concave downward. (Enter your answers using interval notation. If the answer cannot be expressed as an interval, enter EMPTY or ∅.)

g(x) = 2x3 − 4x
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Expert Answer

Step 1

Given, function

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g(x) 2x-4x

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Step 2

In order to finding concave up and concave down, first finding the inflection points.

Inflection points are find using second derivative of function equal to zero.

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d (2x2 - 4x) g'(x)=2x3 dx 8'(x)=(6x-4) d(6x-4) 8"(x) dx = 12x

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Step 3

For inflection...

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g "(x)0 12x 0 x 0 is the inflection point.

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Tagged in

Math

Calculus

Derivative