How to find inflection points from second derivative

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Calculus 1 : Points of Inflection

The derivative is y' = 15x2 + 4x − 3. The second derivative is y'' = 30x + 4. And 30x + 4 is negative up to x = −4/30 = −2/15, positive from there onwards. So: f (x) is concave downward up to x =

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Inflection Points

The second derivative of the function is f” (x) = 12x 2 – 48 Set f” (x) = 0, 12x 2 – 48 = 0 Divide by 12 on both sides, we get x 2 – 4 = 0 x 2 = 4 Therefore, x = ± 2 To check or x = 2, substitute x= 1
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Learn how to find the points of inflection for an equation

Analyzing the second derivative to find inflection points. Learn how the second derivative of a function is used in order to find the function's inflection points. Learn which common mistakes

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